question_answer

Voltmeters \[{{V}_{1}}\] and \[{{V}_{2}}\] are connected in series across a D.C. line. \[{{V}_{1}}\] reads 80 V and has a per volt resistance of \[200\Omega \],  \[{{V}_{2}}\]has a total resistance of\[32\Omega \]. The line voltage is

A)  \[120V\]                             

B)  \[160\,V\]

C)  \[220\,V\]           

D)         \[240\,V\]  

Correct Answer: D

Solution :

 The circuit is as shown below Here, \[{{R}_{1}}=\]resistance per unit volt\[\times \]total volume                  \[=200\times 80=16,000=16k\]                 \[{{R}_{2}}=32k\](given) Now,     \[{{V}_{1}}=\left( \frac{V}{{{R}_{1}}+{{R}_{2}}} \right){{R}_{1}}\] or            \[V={{V}_{1}}\times \left( \frac{{{R}_{1}}+{{R}_{2}}}{{{R}_{1}}} \right)=\frac{80\times 48}{16}\]                    \[=80\times 3=\mathbf{240}\]