Resistance

We use the formula for resistance:
Rearranging to solve for resistivity (ρ):
Given:
,


Substitute the values:

The correct option is (B):

We are given energy and charge:

The correct option is (B):

Let the two resistances be and . Given: Ω — (1) When connected in parallel, the equivalent resistance is: Substitute values:

The correct option is (B):

Step 1: Recall the formula for the resistance of a wire.

The resistance of a wire is given by:

where:

• is the resistivity of the material (a constant for a given material),
• is the length of the wire, and
• is the cross-sectional area of the wire.

Step 2: Analyze the effect of doubling the length and area.

If the length is doubled, the new length becomes . If the cross-sectional area is doubled, the new area becomes . Substituting these into the formula for resistance:

Simplify the expression:

Step 3: Compare the new resistance with the original resistance.

The new resistance is equal to the original resistance . Thus, the resistance remains unchanged.

Final Answer: The resistance will , which corresponds to option .

Step 1: Recall the resistivity values of common materials.

• Air: Air is an insulator and has a very high resistivity, typically on the order of to . This is much higher than .
• Glass: Glass is also an insulator and has a resistivity in the range of to . A value of falls within this range.
• Rubber: Rubber is another insulator with resistivity values typically ranging from to , which is higher than .
• Iron: Iron is a conductor and has a very low resistivity, approximately , which is far lower than .

Step 2: Match the resistivity value to the correct material.

The resistivity value corresponds to glass, as it falls within the typical resistivity range for glass.

Final Answer: The material is , which corresponds to option .

Step 1: Analyze the arrangement of resistors.

The four resistors form a parallelogram, which can also be thought of as a combination of two parallel branches, each containing two resistors in series. Let the resistors be labeled as follows:

• Resistors and are in one branch (series).
• Resistors and are in the other branch (series).

Step 2: Calculate the resistance of each branch.

In each branch, the two resistors are in series. The equivalent resistance of two resistors in series is the sum of their resistances. Thus:

Similarly, for the second branch:

Step 3: Combine the two branches in parallel.

The two branches are connected in parallel. The equivalent resistance of two resistors in parallel is given by:

Substitute and :

Solve for :

Final Answer: The equivalent resistance between any two opposite corners is , which corresponds to option .

Correct answer: semiconductors

Explanation:
Semiconductors are materials whose electrical conductivity lies between that of conductors and insulators. They are widely used in electronic components like diodes, transistors, and integrated circuits (ICs).

Common semiconductor materials include silicon and germanium.

- Conductors (like copper) are used for wiring, not for making active electronic components.
- Insulators block current and are used for insulation.
- Alloys may be used for some components but are not suitable for diodes and transistors.

Hence, the correct answer is: semiconductors.

Correct answer: passing through origin

Explanation:
According to Ohm's Law, the relationship between potential difference and current is given by:
or equivalently, This equation represents a linear relationship between current and voltage. When potential difference (V) is plotted on the X-axis and current (I) on the Y-axis, the graph is a straight line passing through the origin, because when , .

Hence, the correct answer is: passing through origin.

Correct answer: insulators

Explanation:
Materials with resistivity in the range of to are called insulators.

Insulators offer very high resistance to the flow of electric current, making them ideal for preventing current flow. Common examples include rubber, glass, and plastic.

Comparison:
- Conductors:
- Semiconductors: to
- Insulators: to

Therefore, the correct answer is: insulators.

For resistors connected in series, the total or equivalent resistance is simply the sum of the individual resistances: Given:
,
,
.
Substituting the values: Thus, the equivalent resistance is .

The correct option is (A):

The resistance of conductors like copper increases with temperature because of increased collisions between electrons and atoms, which hinders the flow of electric current. On the other hand, for semiconductors like germanium, the resistance decreases with an increase in temperature due to the increased number of charge carriers available at higher temperatures.

The correct option is (A): increases, decreases

The resistivity of a wire is related to its resistance , length , and area of cross-section by the formula: We are given:
Resistance ,
Length ,
Area of cross-section .
Rearranging the formula to solve for resistivity : Substituting the known values: Thus, the resistivity of the wire is .

The brightness of a bulb depends on the power it dissipates, which is given by the formula: Where:
is the power (brightness),
is the voltage,
is the resistance.
From the formula, we can see that for a constant voltage, the power (brightness) is inversely proportional to the resistance. This means that the bulb with higher resistance will glow dimmer, and the one with lower resistance will glow brighter. Therefore, the dimmer bulb has higher resistance compared to the brighter bulb.

The correct option is (B): Dim bulb

In a series circuit, the total resistance is the sum of individual resistances. The total resistance is: The total current in the circuit is given by Ohm's law: Now, to find the potential difference across the 2 resistor, we use Ohm's law again:

The correct option is (A):

We are given that the bulb is marked with a power of 100 W and a voltage of 240 V. The resistance of the bulb can be found using the formula: Where:
is the power (100 W),
is the voltage (240 V),
is the resistance.
Rearranging the formula to solve for : Substitute the values: Thus, the resistance of the bulb is 576 ohms.

The correct option is (D):

In this problem, four resistors are arranged in the shape of a parallelogram.
The resistors are of equal value , and we are asked to determine the equivalent resistance between two opposite corners.
We can simplify the problem by observing that the resistors can be grouped into two sets of parallel resistors.
Let’s label the resistors as , each with a resistance of .
Resistors and are in parallel.
Resistors and are also in parallel.
The formula for two resistors in parallel is: For : For : Now, the two parallel resistors are in series, and the total equivalent resistance is the sum of these two resistances:

The correct option is (B):

When two resistors are connected in parallel, their equivalent resistance can be calculated using the formula:

$ and .

Substituting the values:

\) :

\) $

Thus, the correct answer is .

To find the resistance of a wire, we use the formula:

where is the specific resistance of the material, is the length of the wire, and is the cross-sectional area.

Given:

Insert these values into the formula:

Simplify the expression:

Thus, the resistance of the wire is .

The resistance (R) of a conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A).

$ \rho R \propto l$.

Step 1: Recall the properties of magnetic field lines.
Magnetic field lines form closed loops, originate from the north pole and terminate at the south pole outside a magnet, and continue from the south pole to the north pole inside the magnet. The density of lines indicates field strength, and they never intersect.

Step 2: Evaluate each statement.
(1) Correct: Magnetic field lines are indeed closed curves.
(2) Wrong: Inside a magnet, field lines go from south to north. Outside, they go from north to south.
(3) Correct: Closer lines indicate a stronger magnetic field.
(4) Correct: Magnetic field lines never intersect.

Step 3: Identify the wrong statement.
Statement (2) is incorrect.

Step 1: Recall the relationship between resistance, resistivity, length, and cross-sectional area of a conductor.
The resistance of a conductor is given by the formula: where is the electrical resistivity of the material, is the length of the conductor, and is the cross-sectional area of the conductor.

Step 2: Rearrange the formula to solve for resistivity .

Step 3: Identify the SI units of resistance, area, and length.
Resistance is measured in Ohms ( ).
Cross-sectional area is measured in square meters ( ).
Length is measured in meters ( ).

Step 4: Substitute the SI units into the formula for resistivity. The SI unit of electrical resistivity is Ohm-meter ( ).