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) $$\frac { R } { 4 }$$ .
B)R.
C) $$\frac { N R } { 4 }$$ .
D)NR.
E)4NR.

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) $$\frac { R } { 4 }$$ . 
B)R. 
C) $$\frac { N R } { 4 }$$ . 
D)NR. 
E)4NR.

Quizplus · Accepted Answer

By observing the circuit, we can see that the middle resistor is in parallel with the two resistors on the right side. Therefore, the equivalent resistance of these three resistors is:
R//R//R = R/3
Next, we can see that this equivalent resistance is in series with the resistor on the left side. Therefore, the total equivalent resistance is:
R/3 + R = 4R/3
Therefore, the answer is C) 4NR/3, since there are N resistors each of resistance R in the circuit.

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