Electricity

Concept: To find the total current, we first need to find the total equivalent resistance ( ) of the circuit. Then, using Ohm's Law ( ), we can find the total current . The diagram shows and are connected in parallel, and this parallel combination is connected in series with . The voltage of the source is 6V. Step 1: Calculate the equivalent resistance of the parallel combination of and Let be the equivalent resistance of and in parallel. The formula for two resistors in parallel is . Given and . To add these fractions, find a common denominator, which is 24. So, . Step 2: Calculate the total equivalent resistance ( ) of the circuit The resistor is in series with the parallel combination . For resistors in series, the total resistance is the sum of individual resistances. Given and we found . Step 3: Calculate the total current ( ) flowing through the circuit using Ohm's Law Given voltage of the source, . Total equivalent resistance, . Using Ohm's Law, : The total current flowing through the circuit is 0.5 A. This matches option (4).

Concept: The electrical resistance ( ) of a conductor is a measure of its opposition to the flow of electric current. Several factors influence this resistance. Step 1: Factors affecting the resistance of a conductor The resistance of a conductor is given by the formula: where:
is the resistance.
(rho) is the resistivity (or specific resistance) of the material of the conductor. Resistivity is an intrinsic property of the material itself (e.g., copper has low resistivity, nichrome has higher resistivity).
is the length of the conductor. Resistance is directly proportional to the length; longer conductors offer more resistance.
is the area of cross-section of the conductor. Resistance is inversely proportional to the cross-sectional area; thicker wires (larger area) offer less resistance. Additionally, the resistance of most materials also depends on temperature. For most conductors, resistance increases with increasing temperature. Step 2: Analyzing the options
(1) length ( ): Yes, resistance is directly proportional to length ( ).
(2) area of cross section ( ): Yes, resistance is inversely proportional to the area of cross-section ( ).
(3) material ( ): Yes, the resistivity ( ) is a property of the material, and resistance depends on resistivity. Different materials have different resistivities.
(4) all the above: Since resistance depends on length, area of cross-section, and the material (which determines resistivity), this option is correct. (Temperature is another factor, but it's not among the options here). Therefore, the resistance of a conductor depends on its length, area of cross-section, and the material it is made of.

Concept: Electric power ( ) in a circuit is the rate at which electrical energy is transferred. There are several common formulas to calculate power, derived from the basic definition and Ohm's Law ( ). Step 1: Basic Formula for Electric Power The fundamental formula for electric power is: where is the voltage (potential difference) across the component and is the current flowing through it. This matches option (3), so VI {does} represent electric power. Step 2: Derive other power formulas using Ohm's Law ( )
Substitute into : This matches option (1), so {does} represent electric power. This form is often used to calculate power dissipated as heat in a resistor.
Substitute (from Ohm's Law) into : This matches option (4), so {does} represent electric power. Step 3: Analyze the remaining option The options that correctly represent electric power are:
(Option 3)
(Option 1)
(Option 4) The remaining option is:
(2) : This expression does not correspond to any standard formula for electric power. The resistance term is squared, which is incorrect. Step 4: Conclusion The term that does not represent electric power in a circuit is .

Concept: Different electrical instruments are designed to measure specific electrical quantities. Potential difference, also known as voltage, is one such quantity. Step 1: Understanding Potential Difference (Voltage) Potential difference (voltage) is the difference in electric potential energy per unit charge between two points in an electric circuit. It is what drives the electric current. Its SI unit is the Volt (V). Step 2: Analyzing the functions of the listed devices
(1) Energy meter (or Watt-hour meter): This device measures the total amount of electrical energy consumed over a period of time. The unit is typically kilowatt-hours (kWh).
(2) Ammeter: An ammeter is an instrument used to measure electric current flowing through a circuit. It is connected in series in the circuit. Its unit is Ampere (A).
(3) Galvanometer: A galvanometer is a sensitive instrument used to {detect} and indicate the presence of small electric currents. It can be modified to make ammeters and voltmeters. On its own, it indicates current, not directly potential difference as a calibrated value.
(4) Voltmeter: A voltmeter is an instrument specifically designed to measure the electric potential difference (voltage) between two points in a circuit. It is connected in parallel across the component or points whose voltage is to be measured. Its unit is Volt (V). Step 3: Identifying the correct device The device used for measuring potential difference (voltage) is the voltmeter.

Concept: An ammeter is an instrument used to measure the electric current flowing through a component or a part of an electrical circuit. The way it is connected is crucial for accurate measurement and proper circuit operation. Step 1: What does an ammeter measure? An ammeter measures the flow of electric charge, i.e., the electric current (in Amperes). To measure the current flowing {through} a component, all that current must pass through the ammeter. Step 2: How to connect an ammeter to measure current THROUGH a component To ensure all the current flowing through a specific part of the circuit also flows through the ammeter, the ammeter must be placed directly in the path of that current. This means the ammeter is connected in series with the component or part of the circuit whose current is to be measured. If an ammeter is connected in series, the circuit is broken at one point, and the ammeter is inserted to complete the circuit. Step 3: Why not in parallel? If an ammeter were connected in parallel with a component, it would offer an alternative path for the current. An ideal ammeter has very {low} internal resistance (to avoid significantly altering the total resistance of the circuit and thus the current it's trying to measure). If connected in parallel across a component (which usually has some resistance), a very large current would flow through the low-resistance ammeter, potentially damaging the ammeter and drawing excessive current from the source. (A voltmeter, which measures voltage, is connected in parallel and has very high resistance). Step 4: Analyzing the options
(1) parallel: Incorrect. This is how a voltmeter is connected.
(2) series: Correct. An ammeter is connected in series to measure the current flowing through that part of the circuit.
(3) in any way: Incorrect. The connection method is specific for correct measurement and safety.
(4) none of these: Incorrect, as series is the correct method. Therefore, an ammeter is used in a circuit in series.

Concept: This question asks to identify the physical quantity represented by the unit Joule per Coulomb (J/C). We need to recall the definitions of various electrical quantities and their units. Step 1: Define the units involved
Joule (J): The SI unit of energy or work.
Coulomb (C): The SI unit of electric charge. So, Joule/Coulomb means Energy per unit Charge (or Work done per unit Charge). Step 2: Recall the definitions of the quantities in the options
Volt (V): The SI unit of electric potential difference (voltage) or electromotive force (emf). Electric potential difference ( ) between two points is defined as the work done ( ) per unit charge ( ) to move a charge from one point to another. The unit of work ( ) is Joule (J), and the unit of charge ( ) is Coulomb (C). Therefore, the unit of Volt is Joule/Coulomb (J/C).
Ampere (A): The SI unit of electric current ( ). Current is the rate of flow of charge.
Watt (W): The SI unit of power ( ). Power is the rate at which work is done or energy is transferred. Also, .
Ohm ( ): The SI unit of electrical resistance ( ). From Ohm's Law, (Volt/Ampere). Step 3: Identify the quantity represented by Joule/Coulomb From the definition of electric potential difference (voltage), its unit is Joule per Coulomb. Therefore, Joule/Coulomb represents volt.

Concept: Electrical energy consumed is calculated by multiplying the power of the appliance by the time for which it is used. Energy ( ) = Power ( ) Time ( ). If power is in watts (W) and time is in hours (h), the energy will be in watt-hours (Wh). If power is in kilowatts (kW) and time is in hours (h), the energy will be in kilowatt-hours (kWh). 1 kilowatt (kW) = 1000 watts (W). Step 1: Identify the given values
Power of the bulb,
Time for which it runs, The options are in kWh, so it's convenient to convert power to kilowatts first. Step 2: Convert power from watts to kilowatts Step 3: Calculate the electrical energy consumed in kWh Using the formula : Alternative calculation in Watt-hours first: Energy in Wh = . To convert Wh to kWh, divide by 1000 (since 1 kWh = 1000 Wh): Energy in kWh = . The electrical energy consumed is 3 kWh. This matches option (1).

Concept: Electrical wiring in domestic circuits uses a color-coding system for wires to ensure safety and proper connections. These conventions can vary by region, but there are common standards. Step 1: Understanding the main wires in a domestic AC circuit A typical single-phase AC domestic circuit has three main types of wires:
Live Wire (or Phase/Hot Wire): Carries the alternating current from the source to the appliance. It is at a high potential relative to the neutral and earth.
Neutral Wire: Provides the return path for the current from the appliance back to the source. It is maintained at or near zero potential (earth potential).
Earth Wire (or Ground Wire): A safety wire connected to the metallic body of an appliance and then to the ground. It provides a low-resistance path for current to flow to the earth in case of a fault (e.g., if the live wire touches the appliance casing), preventing electric shock. Step 2: Common Color Coding Conventions Color codes can vary by country and over time.
Old UK / India Convention (still widely found):
Live: Red
Neutral: Black
Earth: Green
New International (IEC) / Harmonized European Convention (also used in modern installations in India and other places):
Live: Brown (for single-phase)
Neutral: Blue
Earth: Green-and-Yellow striped
North America (e.g., USA, Canada):
Live (Hot): Black (or Red for a second hot wire in 240V circuits)
Neutral: White
Ground: Green, or Green-and-Yellow striped, or bare copper. Step 3: Determining the color of the neutral wire based on options and common knowledge The question asks for the color of the neutral wire in a "domestic circuit" without specifying a region. Given the options: (1) black (2) red (3) blue (4) green
If we consider the older convention (still prevalent in many existing installations in places like India), the neutral wire is Black.
If we consider the new IEC convention, the neutral wire is Blue. Since "Black" is option (1) and "Blue" is option (3), and the image circles option (1) "black", it implies the question likely refers to the older, very common convention where neutral is black. Red is live (old convention). Green is earth. Therefore, based on the older common convention (and the circled answer), the color of the neutral wire is black.

Concept: The heating effect of electric current, also known as Joule heating or resistive heating, is the phenomenon where the passage of an electric current through a conductor produces heat. This effect is described by Joule's law, , where is power dissipated as heat, is current, and is resistance. Step 1: Understanding the application of the heating effect The heating effect of current is utilized in devices where the primary purpose is to generate heat or light (as a byproduct of intense heat). Step 2: Analyzing the options
(1) Electric generator: A generator converts mechanical energy into electrical energy. While some heat is produced due to internal resistance (an undesired energy loss), its primary function is not based on the heating effect.
(2) Bulb (Incandescent bulb): An incandescent light bulb works by passing current through a thin filament. The filament has high resistance, and due to the heating effect, it becomes extremely hot (incandescent) and emits light. This is a direct application of the heating effect. Other heating devices like electric heaters, toasters, electric irons also work on this principle.
(3) Battery: A battery is a source of electrical energy, converting chemical energy into electrical energy. Heat can be generated within a battery due to internal resistance, especially during high current draw or charging/discharging, but this is usually an undesirable side effect and not its primary purpose.
(4) Electric motor: An electric motor converts electrical energy into mechanical energy (motion). Similar to a generator, heat produced due to winding resistance is an energy loss and not the intended useful output. Step 3: Identifying the device that primarily uses the heating effect Among the given options, the bulb (specifically an incandescent bulb) is designed to utilize the heating effect of current to produce light. Many other common heating appliances also rely on this effect.

Concept: A fuse wire is a safety device used in electrical circuits to protect appliances from damage due to excessive current (overcurrent conditions like short circuits or overloads). Its operation relies on the heating effect of current. Step 1: Understanding the function of a fuse wire When an excessively high current flows through a circuit, the fuse wire is designed to heat up rapidly and melt. This melting breaks the circuit, stopping the flow of current and preventing damage to the connected appliances or wiring. Step 2: Desired properties of a fuse wire material For a fuse wire to function effectively as a safety device, it must have: (A) Low Melting Point: This is crucial. The wire must melt at a temperature that is reached when a dangerous level of current flows, but before the circuit wires or appliances get dangerously hot. If the melting point is too high, the fuse won't blow (melt) quickly enough to protect the circuit. (B) High Resistivity (or Resistance for a given length/thickness): The heating effect is given by . For a given current ( ), a higher resistance ( ) will lead to more heat being generated ( ). This helps the fuse wire heat up and melt quickly when an overcurrent occurs. So, higher resistivity compared to the main circuit wires is desirable. (C) Low cost and resistance to oxidation/corrosion under normal conditions are also practical considerations. Comparing the primary safety characteristics, the low melting point is the most critical for the fuse to act as a protective break. High resistance contributes to the heating, but without a low melting point, it won't melt appropriately. Step 3: Analyzing the options
(1) high melting point: Incorrect. This would prevent the fuse from melting and breaking the circuit during an overcurrent.
(2) low melting point: Correct. This ensures the fuse wire melts and breaks the circuit before excessive current can cause significant damage.
(3) high resistance: This property is also desirable for a fuse wire (relative to the circuit wires) because it helps the wire to heat up quickly ( ). Materials like tin-lead alloy are used, which have higher resistivity than copper (used for circuit wires) and a low melting point. While important, the "low melting point" is the defining characteristic for its safety function. If both were equally weighted as essential properties, the question would be ambiguous. However, the primary purpose is to melt.
(4) none of these: Incorrect. Considering the primary function, "low melting point" is the most critical characteristic. Option (3) "high resistance" is also a desirable property, but the melting is the key action. Typically, questions prioritize the low melting point.

Concept: The electron is a subatomic particle with a fundamental electric charge. This charge is known as the elementary charge, often denoted by . Step 1: Recalling the value of the elementary charge The magnitude of the charge on a single electron (and also on a proton) is a fundamental physical constant. The electron carries a negative charge, while a proton carries a positive charge of the same magnitude. The value of this elementary charge is approximately Coulombs. For most introductory purposes, this is rounded to Coulombs. Step 2: Understanding the options The question asks for "The charge of electron". Since an electron is negatively charged, its charge is actually . However, multiple-choice questions often ask for the magnitude of the charge. All options are positive, implying the magnitude is being sought.
(1) : This matches the commonly accepted magnitude of the elementary charge.
(2) : This is , which is 10 times too large.
(3) : This is , which is 10 times too small.
(4) : This is , which is significantly different. Step 3: Identifying the correct value The magnitude of the charge of an electron is .

Concept: A voltmeter is an instrument used to measure the electric potential difference (voltage) between two points in a circuit. How it's connected is crucial for a correct measurement and for the proper functioning of the circuit. Step 1: What does a voltmeter measure? A voltmeter measures the difference in electrical potential (voltage drop) {across} a circuit component (like a resistor, bulb) or between any two points. Step 2: How to connect a voltmeter to measure voltage ACROSS a component To measure the voltage across a component, the voltmeter must be connected so that its terminals are at the same two points as the component whose voltage is being measured. This means the voltmeter is connected in parallel with that component.
One terminal of the voltmeter is connected to one end of the component.
The other terminal of the voltmeter is connected to the other end of the component. This way, the voltmeter experiences the same potential difference as the component. Step 3: Why not in series? If a voltmeter were connected in series with a component, it would be part of the main current path. An ideal voltmeter has very high internal resistance (to draw minimal current and not disturb the circuit it's measuring). If placed in series, this high resistance would significantly reduce the current in the circuit, altering the very voltage it's trying to measure and affecting the circuit's operation. (An ammeter, which measures current, is connected in series and has very low resistance). Step 4: Analyzing the options
(1) parallel: Correct. A voltmeter is connected in parallel across the points where voltage is to be measured.
(2) series: Incorrect. This is how an ammeter is connected.
(3) in any way: Incorrect. The connection method is specific.
(4) none of these: Incorrect, as parallel is the correct method.

Concept: Electric current ( ) is defined as the rate of flow of electric charge ( ) per unit time ( ). The relationship is . Step 1: Given information
Current ( ) =
Time ( ) = We need to find the amount of electrical charge ( ). Step 2: Convert time to SI units (seconds) The SI unit for time in this formula is seconds. Step 3: Use the formula relating current, charge, and time The formula is . We need to find , so we rearrange the formula: Step 4: Calculate the charge ( ) Substitute the values of and (in seconds) into the formula: (Note: is the same as half of 600). The amount of electrical charge that flows through the filament is . This matches option (1).

Concept: Electric power ( ) is the rate at which electrical energy is consumed or produced. It's related to voltage ( ) and current ( ). Step 1: Given information
Voltage ( ) =
Current ( ) = Step 2: Formula for Electric Power The formula to calculate electric power when voltage and current are known is: Where is in watts (W), in volts (V), and in amperes (A). Step 3: Calculate the power Substitute the given values into the formula: (Note: Multiplying by 0.50 is the same as dividing by 2). The power of the bulb is . This matches option (1).

Concept: Different electrical devices have specific functions related to electric current. This question asks about the device that *produces* current. Step 1: Understanding the functions of the listed devices
(1) Generator: A generator converts mechanical energy (like rotation from a turbine) into electrical energy. This process *produces* an electric current. It works based on electromagnetic induction.
(2) Galvanometer: A galvanometer is a sensitive instrument used to *detect* and measure small electric currents. It does not produce current.
(3) Ammeter: An ammeter is an instrument used to *measure* the magnitude of electric current flowing in a circuit. It does not produce current.
(4) Motor (Electric Motor): An electric motor converts electrical energy into mechanical energy (motion). It *uses* electric current, it doesn't produce it. Step 2: Identifying the current-producing device From the descriptions, the generator is the device that produces electric current.

Concept: A short circuit is a low-resistance path unintentionally created in an electrical circuit. Ohm's Law ( ) helps understand its effect on current. Step 1: What is a short circuit? A short circuit occurs when the current bypasses its intended path (the load, like a bulb or appliance) and instead flows through an alternative path with very low resistance. For example, if the live and neutral wires touch directly. Step 2: Applying Ohm's Law ( )
is the voltage of the source (e.g., 220V).
is the resistance of the circuit.
is the current flowing. In a normal circuit, the load provides a certain resistance ( ). In a short circuit, the resistance of the path ( ) becomes extremely small (close to zero). Step 3: Effect on Current Since : If becomes very small (as in ), and remains constant, the current must become very large. . Since is tiny, is huge. This is why the current "increases heavily." Step 4: Consequences This large current can cause overheating of wires (due to heating effect), leading to melting insulation, fires, or damage to the power source. Protective devices like fuses or circuit breakers are designed to break the circuit if such high currents occur.

Step 1: Understand the function of a voltmeter.
A voltmeter is an instrument used to measure the potential difference (voltage) between two points in an electrical circuit. To measure voltage, a voltmeter must be connected in parallel across the component whose voltage is to be measured. Step 2: Consider how a voltmeter should ideally interact with a circuit.
For a voltmeter to accurately measure the voltage across a component without altering the current distribution or voltage drop in the rest of the circuit, it should draw negligible current from the circuit. Step 3: Relate current drawn to resistance (Ohm's Law).
According to Ohm's Law, , where is voltage, is current, and is resistance. If the voltmeter draws negligible current ( ) for a given voltage ( ), its resistance ( ) must be very high. Step 4: Define "ideal" voltmeter resistance.
In an ideal scenario, a voltmeter draws no current at all to ensure perfect measurement accuracy. For to be zero while is non-zero, the resistance ( ) must be infinitely large. Step 5: Evaluate the given options in the context of an ideal voltmeter.

(1) : This is a finite, relatively low resistance, which would draw significant current and affect the circuit being measured.
(2) Infinite: An infinite resistance ensures that no current flows through the voltmeter, thus not disturbing the circuit it is measuring. This is the characteristic of an ideal voltmeter.
(3) Low: A low resistance would cause the voltmeter to act like a short circuit, diverting current and significantly altering the voltage being measured.
(4) Zero: Zero resistance would mean the voltmeter acts as a perfect short circuit, drawing maximum current and effectively shorting out the component it's meant to measure the voltage across. Step 6: Conclude the correct resistance for an ideal voltmeter.
The resistance of an ideal voltmeter is infinite. (2) Infinite

Step 1: Recall the charge of a single electron.
The charge of a single electron ( ) is approximately Coulombs (C). Step 2: Understand the relationship between total charge, number of electrons, and charge per electron.
The total charge ( ) is equal to the number of electrons ( ) multiplied by the charge of a single electron ( ). So, . Step 3: Rearrange the formula to find the number of electrons.
To find the number of electrons ( ), we can rearrange the formula as: Step 4: Substitute the given values into the formula.
We are given that Coulomb (C) and C. Step 5: Calculate the number of electrons.
Rounding to two decimal places, this is approximately . Step 6: Compare with the given options.
(1) : This matches our calculated value.
(2) : This is the magnitude of the charge of a single electron, not the number of electrons in one coulomb.
(3) : This value is incorrect.
(4) : This value is incorrect.
(1) }