Current Electricity 4 Question 8

8. A galvanometer having a resistance of $20 \Omega$ and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt is

(2019 Main, 11 Jan II)

(a) $100 \Omega$

(b) $125 \Omega$

(c) $120 \Omega$

(d) $80 \Omega$

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Solution:

  1. Resistance of galvanometer, $(G)=20 \Omega$

Number of divisions on both side $=30$

Figure of merit $=0.005$ ampere/division

$\therefore$ Full scale deflection current $\left(I _g\right)$

$=$ Number of divisions $\times$ figure of merit

$$ \Rightarrow \quad I _g=30 \times 0.005=0.15 A $$

Now, for measuring $15 V$ by this galvanometer, let we use a resistance of $R$ ohm in series with the galvanometer.

$\therefore$ Effective resistance of voltmeter, $R _{\text {eff }}=R+20$

As,maximum potential measured by voltmeter.

or

$$ \begin{aligned} & V=I _g \cdot R _{\text {eff }} \text { or } 15=0.15(R+20) \\ & R+20=100 \text { or } R=80 \Omega \end{aligned} $$



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