question_answer

Consider the following statements regarding the network shown in the figure:

1. The equivalent resistance of the network between points A and B is \[\left( \frac{4}{3}R \right)\].

2. The current in resistor 3R is zero.

3. The potential difference across R is equal to the potential difference across 2R.

Which of the above statement(s) is/are correct?

A) 1 only                          

B) 2 only                    

C)      2 and 3                        

D) 1, 2 and 3                    

Correct Answer: D

Solution :

(d) 1, 2 and 3                                            The given network represent a Wheatstone bridge         \[\because \frac{R}{2R}=\frac{R}{2R}\] The resistance 3R is ineffective.                           The equivalent circuit reduces to the circuit shown in the figure.                                                   Equivalent Resistance,                      \[{{R}_{eq}}=\frac{2R\times 4R}{2R+4R}=\frac{8{{R}^{2}}}{6R}=\frac{4R}{3}\] So, option (1) is correct.                                      As Wheatstone bridge is balanced, no current flows through 3R, i.e., current in 3R is zero.                                  So, option (2) is correct.                                     Voltage across parallel resistances is same, so option (3) is also correct.