Question

The ratio of resistances of two copper wires of the same length and of same cross sectional area when connected in series to that when connected in parallel is

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 4 : 1
• E. 1 : 4

Hint:

Two equal resistors: series → double, parallel → half.

Answer 1

The Correct Option is D

Understanding the Concept: Resistance: \[ R = \rho \frac{L}{A} \] Same material and dimensions → both resistances equal \(R\).

Step 1: Series combination. \[ R_s = R + R = 2R \]

Step 2: Parallel combination. \[ R_p = \frac{R \cdot R}{R + R} = \frac{R}{2} \]

Step 3: Take ratio. \[ \frac{R_s}{R_p} = \frac{2R}{R/2} = 4 \]

Step 4: Final Answer. \[ \boxed{4:1} \]