A circuit consists of 2N resistors, all of resistance R, connected as shown below.A potential difference V is applied to one end, and the other end is at ground potential.The equivalent resistance of the circuit is:
B)R.
D)NR.
E)2NR.

Question

A circuit consists of 2N resistors, all of resistance R, connected as shown below.A potential difference V is applied to one end, and the other end is at ground potential.The equivalent resistance of the circuit is: 
B)R. 
D)NR. 
E)2NR.

Quizplus · Accepted Answer

The circuit can be divided into two parts: a left half and a right half. Each half contains N resistors in parallel, which combine to an equivalent resistance of R/N. The two halves are then connected in series, adding their resistances to give a total circuit resistance of 2R/N. Multiplying by the 2N resistors in the circuit gives an overall equivalent resistance of 2NR/N = 2R. Therefore, the answer is E.

A Circuit Consists of 2N Resistors, All of Resistance R