Question

Ten resistors, each having resistance of $6\text{ }\Omega$, are connected in a circuit. Then the ratio of maximum current to the minimum current that can flow through the circuit is:

• A. $10:1$
• B. $1:10$
• C. $100:1$
• D. $1:100$

Hint:

For $N$ identical resistors, the ratio of maximum to minimum resistance is:
$\frac{R_{\text{max}}}{R_{\text{min}}} = N^2$.
Since current is inversely proportional to resistance, the ratio of currents is also:
$\frac{I_{\text{max}}}{I_{\text{min}}} = N^2 = 10^2 = 100$.
This rule holds true regardless of the individual resistance values.

Answer 1

The Correct Option is C

Step 1: Use the general n-resistor result instead of computing each combination.
For $n$ identical resistors of resistance $R$, the minimum equivalent resistance (all parallel) is $R/n$ and the maximum equivalent resistance (all series) is $nR$.
Step 2: Write the current ratio directly.
At a fixed voltage $V$, current is $I = V/R_{\text{eq}}$, so the maximum current comes from the smallest resistance and vice versa: \[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{R_{\text{eq,max}}}{R_{\text{eq,min}}} = \frac{nR}{R/n} = n^2 \]
Step 3: Substitute n = 10. \[ \frac{I_{\text{max}}}{I_{\text{min}}} = 10^2 \] \[ \boxed{100:1} \]