Electrical Circuits

From the graph: The threshold frequency ( ) is the x-intercept of the graph: The work function ( ) is given by: Converting to eV: \item From the slope of the graph, Planck's constant is:

From de Broglie wavelengths formula: where is the mass and is the kinetic energy. For the same wavelength: Since the proton has less mass than the neutron, its kinetic energy will be greater for the same wavelength.

Given:
Resistance , Inductive voltage , Capacitive voltage , and source voltage:

(i) Current in the circuit

Step 1: The impedance of the circuit: Since the inductor and capacitor voltages are equal, they cancel each other out, leaving only the resistance.

Step 2: Applying Ohm's law: (ii) The potential across resistance

Solution: Step 1: Using Ohm's law to find the potential across the resistor:

(iii) The phase difference between the potentials across inductor and capacitor

Solution:

Step 1: In an LC circuit, the voltage across the inductor leads the current by , while the voltage across the capacitor lags the current by .

Step 2: Therefore, the phase difference between the inductor and capacitor voltages is:

A resonant circuit is an electrical circuit in which resonance occurs at a particular frequency.

Resonance Condition:

Resonant Frequency:

A cell is a single electrochemical unit that converts chemical energy into electrical energy, while a battery consists of multiple cells connected together to provide higher voltage or current.

Step 1: A cell generates electrical energy from a chemical reaction within a single unit.

Step 2: A battery consists of multiple interconnected cells to provide higher output for more demanding applications.

(i) Series Combination

Solution: In a series combination, the voltages add up while the current remains the same.

Step 1: Cells are connected end-to-end, with the positive terminal of one connected to the negative terminal of the next.

Step 2: The total voltage is:

Step 3: This configuration is useful when high voltage is required, such as in electronic circuits.

(ii) Parallel Combination

Solution: In a parallel combination, the current increases while the voltage remains the same.

Step 1: Cells are connected with all positive terminals together and all negative terminals together.

Step 2: The total current is:

Step 3: This configuration is useful when a higher current capacity is needed, such as in power backup systems.

(iii) Mixed Combination

Solution: Step 1: In mixed combination, cells are connected in both series and parallel configurations.

Step 2: This provides an increase in both voltage and current, depending on the number of cells.

Step 3: It is useful in applications where both high voltage and current are needed, such as in electric vehicles.

i. Internal resistance of cell Step 1: The internal resistance of a cell depends on several factors: - It increases if the distance between electrodes increases.
- It decreases if the cross-sectional area of electrodes increases.
- It depends on the electrolyte's concentration and nature.

ii. Resistance of conductor

Step 1: The resistance of a conductor is given by: where: - is resistance,
- is resistivity,
- is length,
- is cross-sectional area.

Step 2: Factors affecting resistance: - It increases with an increase in length ( ).
- It decreases with an increase in cross-sectional area ( ).
- Different materials have different resistivities.
- Resistance increases with temperature due to an increase in resistivity.

Step 1: An ammeter is designed to measure larger currents with lower resistance, whereas a milli-ammeter measures smaller currents and therefore requires higher sensitivity.

Step 2: Since a milli-ammeter is more sensitive, it has higher internal resistance compared to an ammeter.

Given the circuit, we need to find out the total resistance and the current flowing through the cell. The circuit consists of resistors in both series and parallel combinations.
1. Total Resistance Calculation:
- First, combine the resistors in parallel. The 500 and 750 resistors are in parallel, and the formula for the total resistance in parallel is: Simplifying this: 2. Total Resistance of the Circuit:
- Now, this equivalent resistance (300 ) is in series with the 1000 resistor. The total resistance in series is simply the sum of the resistances: 3. Current Calculation:
- Using Ohm's Law, , we can calculate the current flowing through the circuit. The given voltage is 4.75 V, and the total resistance is 1300 : Thus, the total resistance of the circuit is 1300 , and the current flowing through the cell is approximately 3.65 mA.