question_answer

A battery of e.m.f. 10 V is connected to resistance as shown in figure. The potential difference \[{{V}_{A}}-{{V}_{B}}\] between the points A and B is                            [MP PMT 1994]

A)                    \[-2V\]

B)                    \[2V\]

C)                    \[5V\]

D)                    \[\frac{20}{11}V\]

Correct Answer: B

Solution :

             \[{{R}_{eq}}=5\Omega \], Current \[i=\frac{10}{5}=2A\] and current in each branch = 1A Potential difference between C and A, \[{{V}_{C}}-{{V}_{A}}=1\times 1=1V\] .......(i) Potential difference between C and B, \[{{V}_{C}}-{{V}_{B}}=1\times 3=3V\]  ......(ii) On solving (i) and (ii)  \[{{V}_{A}}-{{V}_{B}}=2\,volt\] Shot Trick : \[({{V}_{A}}-{{V}_{B}})=\frac{i}{2}({{R}_{2}}-{{R}_{1}})=\frac{2}{2}(3-1)=2V\]