A galvanometer has a resistance of 50 Ω and it allows maximum current of 5 mA. It can be converted into voltmeter to measure upto 100 V by connecting in series a resistor of resistance
- 5975Ω
- 20050Ω
- 19950Ω
- 19500Ω
The Correct Option is C
Solution and Explanation
We use the formula for the total resistance \(R\) of the voltmeter:
\[ R = \frac{V}{I} - R_G \]
Where:
- \(V = 100 \, \text{V}\) is the maximum voltage.
- \(I = 5 \times 10^{-3} \, \text{A}\) is the maximum current.
- \(R_G = 50 \, \Omega\) is the resistance of the galvanometer.
Substituting the values:
\[ R = \frac{100}{5 \times 10^{-3}} - 50 = 20000 - 50 = 19950 \, \Omega \]
Thus, the resistance required is \(19950 \, \Omega\), which corresponds to Option (3).
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Assertion (A): The deflection in a galvanometer is directly proportional to the current passing through it.
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Galvanometer:
A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it.
The name "galvanometer" is derived from the surname of Italian scientist Luigi Galvani, who in 1791 discovered that electric current makes a dead frog’s leg jerk.
A spring attached to the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring, and we have the relation:
\[ NBAI = k\phi \]
Where:
- \( N \) is the total number of turns in the coil
- \( A \) is the area of cross-section of each turn
- \( B \) is the radial magnetic field
- \( k \) is the torsional constant of the spring
- \( \phi \) is the angular deflection of the coil
As the current \( I_g \) that produces full-scale deflection in the galvanometer is very small, the galvanometer alone cannot be used to measure current in electric circuits.
To convert a galvanometer into an ammeter (to measure larger currents), a small resistance called a shunt is connected in parallel to the galvanometer.
To convert it into a voltmeter (to measure potential difference), a high resistance is connected in series with the galvanometer.
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