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

In this circuit, it can be observed that all the resistors are connected in parallel between points A and B. 
Therefore, the equivalent resistance of N resistors in parallel is:
R_eq = R/N
Hence, the total current in the circuit will be:
I = V/R_eq = V*N/R
The potential difference across each resistor is the same and is equal to:
V_R = I*R = V/N
Using Ohm's law, this potential difference across each resistor is equal to the current through it multiplied by the resistance:
V_R = I*R = (V/N)*R
Thus, the total resistance of the circuit is the resistance of one resistor multiplied by the number of resistors:
R_tot = V/(I) = V/((V*N/R)*N) = R*N/(N^2) = R/N
Therefore, the equivalent resistance of the circuit is R/N, which is option B.

A Circuit Consists of N Resistors,all of Resistance R,connected as Shown