Two solid conductors are made up of same material have same length and same resistance . One of them has circular crosssection of area `A_1` and other one has square cross section of area `A_2`. RATIO `A_1/A_2`

Options

A. 1.5
B. 1
C. 0.8
D. 2

Answer

To solve the problem, we need to analyze the relationship between the resistance of the two conductors and their cross-sectional areas. Here’s a step-by-step solution:

### Step 1: Understand the relationship between resistance, resistivity, length, and area
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area.

### Step 2: Set up the equations for both conductors
Let’s denote:
- \( R_1 \) for the first conductor (circular cross-section with area \( A_1 \)),
- \( R_2 \) for the second conductor (square cross-section with area \( A_2 \)).

Since both conductors are made of the same material, have the same length, and the same resistance, we can write:
\[ R_1 = R_2 \]
This implies:
\[ \frac{\rho L}{A_1} = \frac{\rho L}{A_2} \]

### Step 3: Simplify the equation
Since \( \rho \) (resistivity) and \( L \) (length) are the same for both conductors, we can cancel them out from both sides of the equation:
\[ \frac{1}{A_1} = \frac{1}{A_2} \]

### Step 4: Rearranging the equation
This can be rearranged to find the ratio of the areas:
\[ A_1 = A_2 \]

### Step 5: Find the ratio \( \frac{A_1}{A_2} \)
Thus, the ratio of the areas is:
\[ \frac{A_1}{A_2} = 1 \]

### Conclusion
The ratio of the cross-sectional areas \( \frac{A_1}{A_2} \) is equal to 1.

### Final Answer
\[ \frac{A_1}{A_2} = 1 \]

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