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
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
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Two equal resistors: series → double, parallel → half.
Updated On: May 8, 2026
- 1 : 1
- 1 : 2
- 2 : 1
- 4 : 1
- 1 : 4
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The Correct Option is D
Solution and Explanation
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: Conclusion. \[ \boxed{4:1} \]
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: Conclusion. \[ \boxed{4:1} \]
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