Question

With a resistance '\(X\)' connected in series with a galvanometer of resistance \(100 \Omega\), it acts as a voltmeter of range 0 - 15 V. To double the range, a resistance of \(1500 \Omega\) is to be connected in series with '\(X\)'. The value of '\(X\)' in \(\Omega\) is

• A. \(1000\)
• B. \(1200\)
• C. \(1400\)
• D. \(1600\)

Hint:

The full-scale current of the galvanometer is fixed: \(V=I_g(G+R_{series})\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
A galvanometer with series resistance acts as a voltmeter. The full-scale current \(I_g\) is the same for both ranges.

Step 2: Key Formula or Approach
Range 1: \(15=I_g(100+X)\). Range 2: \(30=I_g(100+X+1500)\).

Step 3: Detailed Explanation
Divide: \(\dfrac{30}{15}=\dfrac{100+X+1500}{100+X}\).
\[ 2(100+X)=1600+X \Rightarrow 200+2X=1600+X \Rightarrow X=1400\ \Omega \]

Final Answer:
\(X=1400\ \Omega\), option (C). \[ \boxed{1400\ \Omega\ \text{(C)}} \]