Question

Equivalent resistance \( R \) is obtained when \( n \) wires having the same length and same thickness of the same material are joined in parallel. The equivalent resistance on joining them in series will be:

• A. \( nR \)
• B. \( n^2 R \)
• C. \( R/n \)
• D. \( R/n^2 \)

Hint:

Let each wire be \( r \); parallel gives \( r/n = R \) so \( r = nR \), and series gives \( nr \).

Answer 1

The Correct Option is B

Step 1: Note a standard result: for \(n\) identical resistors, the series total is always \(n^2\) times the parallel total. We verify it here.

Step 2: Let one wire have resistance \(r\). Parallel combination of \(n\) equal resistors gives \(R_p = r/n\), and this is the given \(R\), so \(r = nR\).

Step 3: Series combination of the same \(n\) wires gives \(R_s = nr\). Their ratio is \(\dfrac{R_s}{R_p} = \dfrac{nr}{r/n} = n^2\).

Step 4: Therefore \(R_s = n^2 R_p = n^2 R\).

\[\boxed{R_{series} = n^2 R}\]