A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is
A) .
B) .
C) R.
D) NR.
E) 2NR.

Question

A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is 
A) . 
B) . 
C) R. 
D) NR. 
E) 2NR.

Quizplus · Accepted Answer

Using Kirchhoff's laws, we can see that the circuit can be simplified into a parallel combination of two equivalent branches, each consisting of N series resistors of value R. The equivalent resistance of each branch is NR, and the total current flowing through the circuit is V/(2NR). By applying Kirchhoff's current law at the junction of the two branches, we can see that the current flowing through each branch is equal to V/(2NR). Using Ohm's law, we can calculate the potential difference across each resistor in each branch as IR = (V/N)/R = V/(NR). The potential difference across the equivalent resistance of the circuit is therefore (V/N) + (V/N) = 2V/N. Using Ohm's law again, we can calculate the equivalent resistance of the circuit as R_equiv = (2V/N) / (V/(2NR)) = 4R/11N. Since we know that R_equiv = 11R/N, we can solve for N to get N = 44/11 = 4. Therefore, the correct answer is B, 11eb6adc_ee1f_4d2f_b0cf_71207d99bad8_TB8245_11.

A Circuit Consists of N Resistors, All of Resistance R