Question

When two identical resistors are connected in series to an ideal cell, the current through each resistor is \( 2 \) A. If the resistors are connected in parallel to the cell, the current through each resistor is?

• A. \( 4 \) A
• B. \( 2 \) A
• C. \( 8 \) A
• D. \( 1 \) A

Hint:

For resistors in series, the total resistance is \( R_{\text{series}} = R_1 + R_2 \). For resistors in parallel, use \( \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} \).

Answer 1

The Correct Option is A

Step 1: Define resistance in series connection 
Let the resistance of each resistor be \( R \) and the voltage of the ideal cell be \( V \). For two resistors connected in series, the total resistance is: \[ R_{\text{series}} = R + R = 2R \] By Ohm's law, the total current in the series circuit is: \[ I_{\text{total}} = \frac{V}{R_{\text{series}}} = \frac{V}{2R} \] Given that the current through each resistor in series is \( 2 \) A, the total current is also \( 2 \) A: \[ \frac{V}{2R} = 2 \] \[ V = 4R \] 

Step 2: Define resistance in parallel connection 
For two resistors connected in parallel, the equivalent resistance is: \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \] \[ R_{\text{parallel}} = \frac{R}{2} \] By Ohm's law, the total current in the parallel circuit is: \[ I_{\text{total}} = \frac{V}{R_{\text{parallel}}} = \frac{4R}{R/2} = \frac{4R \times 2}{R} = 8 \text{ A} \] Since the current divides equally between the two resistors, the current through each resistor is: \[ I = \frac{I_{\text{total}}}{2} = \frac{8}{2} = 4 \text{ A} \] Thus, the current through each resistor in the parallel connection is \( 4 \) A.