The length of a conductor is halved. Its conductance will be

Options

A. halved
B. unchanged
C. doubled
D. quadrupled

Answer

To solve the problem, we need to understand the relationship between the length of a conductor and its conductance. Here's the step-by-step solution:

### Step 1: Understand the relationship between resistance and conductance
Conductance (C) is defined as the reciprocal of resistance (R):
\[ C = \frac{1}{R} \]

### Step 2: Write the formula for resistance
The resistance (R) of a conductor is given by the formula:
\[ R = \frac{\rho l}{A} \]
where:
- \( \rho \) is the resistivity of the material,
- \( l \) is the length of the conductor,
- \( A \) is the cross-sectional area of the conductor.

### Step 3: Substitute the resistance formula into the conductance formula
Substituting the expression for resistance into the conductance formula, we get:
\[ C = \frac{1}{R} = \frac{A}{\rho l} \]

### Step 4: Analyze the effect of halving the length
If the length \( l \) of the conductor is halved, we can denote the new length as \( l' = \frac{l}{2} \). We can substitute this into the conductance formula:
\[ C' = \frac{A}{\rho l'} = \frac{A}{\rho \left(\frac{l}{2}\right)} \]

### Step 5: Simplify the expression for the new conductance
This simplifies to:
\[ C' = \frac{A}{\rho \left(\frac{l}{2}\right)} = \frac{2A}{\rho l} = 2 \cdot \frac{A}{\rho l} = 2C \]

### Step 6: Conclusion
Thus, when the length of the conductor is halved, the conductance becomes double the original conductance:
\[ C' = 2C \]

### Final Answer
The conductance will be doubled.

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