MHT CET · Physics · Current Electricity
A galvanometer of resistance \(G\) can be converted into a voltmeter of range \(V\) by connecting a resistance \(R\) in series with it. The series resistance required to change its range to \(\frac{V}{3}\) is
- A \(\frac{R-3 G}{4}\)
- B \(\frac{R+G}{3}\)
- C \(\frac{R-G}{2}\)
- D \(\frac{R-2 G}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{R-2 G}{3}\)
Step-by-step Solution
Detailed explanation
Case-1
\(\begin{aligned}
& R=\frac{V}{I_G}-G \\
& \Rightarrow I_G=\frac{V}{R+G}
\end{aligned}\)
Case-2:
\(R^{\prime}=\frac{\left(\frac{V}{3}\right)}{I_G}-G=\frac{\left(\frac{V}{3}\right)}{\left(\frac{V}{R+G}\right)}-G=\left(\frac{R-2 G}{3}\right)\)
\(\begin{aligned}
& R=\frac{V}{I_G}-G \\
& \Rightarrow I_G=\frac{V}{R+G}
\end{aligned}\)
Case-2:
\(R^{\prime}=\frac{\left(\frac{V}{3}\right)}{I_G}-G=\frac{\left(\frac{V}{3}\right)}{\left(\frac{V}{R+G}\right)}-G=\left(\frac{R-2 G}{3}\right)\)
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