question_answer

In the circuit shown in the figure, reading of voltmeter is \[{{V}_{1}}\] when only \[{{S}_{1}}\] is closed, reading of voltmeter is \[{{V}_{2}}\] when only \[{{S}_{2}}\] is closed and reading of voltmeter is \[{{V}_{3}}\] when both \[{{S}_{1}}\] and \[{{S}_{2}}\] are closed. Then-

A) \[{{V}_{3}}>{{V}_{2}}>{{V}_{1}}\] 

B)   \[{{V}_{2}}>{{V}_{1}}>{{V}_{1}}\]

C) \[{{V}_{3}}>{{V}_{1}}>{{V}_{2}}\]             

D) \[{{V}_{1}}>{{V}_{2}}>{{V}_{3}}\]

Correct Answer: B

Solution :

S1 closed \[{{V}_{1}}=\frac{3R}{R+3R}\,\,\,V=\frac{3}{4}\,\,V\,\,=\,\,0.75\,\,V\] S2 closed \[{{V}_{2}}\,=\,\,\frac{6R}{R+6R}\,\,V=0.85\,\,R\] \[{{S}_{1}}\And \text{ }{{S}_{2}}\,\,both\text{ }closed\]   \[{{V}_{3}}=\frac{2R}{R+2R}\,\,\,V=0.67\,V\] \[\therefore \,\,\,{{V}_{2}}>{{V}_{1}}>{{V}_{3}}\]