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
Approach Solution - 1
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).
Approach Solution -2
The problem requires us to find the value of a series resistance needed to convert a given galvanometer into a voltmeter that can measure up to 100 V.
Concept Used:
To convert a galvanometer into a voltmeter, a high resistance, often called a multiplier resistor (\(R_s\)), is connected in series with the galvanometer. The purpose of this series resistor is to limit the current flowing through the galvanometer to its full-scale deflection current (\(I_g\)) when the maximum desired voltage (\(V\)) is applied across the combination.
According to Ohm's law, the total voltage \(V\) across the voltmeter (the series combination of the galvanometer and the resistor) is given by:
where:
\(V\) is the maximum voltage the voltmeter can measure.
\(I_g\) is the current for full-scale deflection of the galvanometer.
\(R_g\) is the internal resistance of the galvanometer.
\(R_s\) is the resistance of the series resistor.
Step-by-Step Solution:
Step 1: Identify and list the given parameters from the problem statement.
Resistance of the galvanometer, \(R_g = 50 \, \Omega\).
Maximum current (full-scale deflection current), \(I_g = 5 \, \text{mA} = 5 \times 10^{-3} \, \text{A}\).
The desired maximum voltage measurement range, \(V = 100 \, \text{V}\).
Step 2: State the formula for the series resistance \(R_s\). We rearrange the main formula \(V = I_g (R_g + R_s)\) to solve for \(R_s\).
\[ \frac{V}{I_g} = R_g + R_s \]Therefore, the required series resistance is:
\[ R_s = \frac{V}{I_g} - R_g \]Step 3: Substitute the given numerical values into the formula to calculate \(R_s\).
\[ R_s = \frac{100 \, \text{V}}{5 \times 10^{-3} \, \text{A}} - 50 \, \Omega \]Step 4: Perform the calculation to find the value of \(R_s\).
First, calculate the ratio \(\frac{V}{I_g}\):
\[ \frac{100}{5 \times 10^{-3}} = \frac{100 \times 1000}{5} = 20 \times 1000 = 20000 \, \Omega \]Now, subtract the galvanometer resistance from this value:
\[ R_s = 20000 \, \Omega - 50 \, \Omega \] \[ R_s = 19950 \, \Omega \]Hence, the resistance that must be connected in series to convert the galvanometer into a voltmeter that can measure up to 100 V is 19950 Ω.
Top Questions on The Moving Coil Galvanometer
- Consider a moving coil galvanometer (MCG):
A : The torsional constant in moving coil galvanometer has dimensions \( [ML^2 T^{-2}] \)
B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C : If we increase the number of turns (N) to its double (2N), then the voltage sensitivity doubles.
D : MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with the galvanometer.
E : Current sensitivity of MCG depends inversely on the number of turns of the coil.
Choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- The Moving Coil Galvanometer
- In a moving coil galvanometer, two moving coils $ M_1 $ and $ M_2 $ have the following particulars: $ R_1 = 5 \, \Omega $, $ N_1 = 15 $, $ A_1 = 3.6 \times 10^{-3} \, \text{m}^2 $, $ B_1 = 0.25 \, \text{T} $ $ R_2 = 7 \, \Omega $, $ N_2 = 21 $, $ A_2 = 1.8 \times 10^{-3} \, \text{m}^2 $, $ B_2 = 0.50 \, \text{T} $ Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $ M_1 $ and $ M_2 $?
- JEE Main - 2025
- Physics
- The Moving Coil Galvanometer
- If the number of turns is increased in any moving coil galvanometer, then its sensitivity
- Bihar Board XII - 2025
- Physics
- The Moving Coil Galvanometer
Assertion (A): The deflection in a galvanometer is directly proportional to the current passing through it.
Reason (R): The coil of a galvanometer is suspended in a uniform radial magnetic field.
- CBSE CLASS XII - 2025
- Physics
- The Moving Coil Galvanometer
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.
- CBSE CLASS XII - 2025
- Physics
- The Moving Coil Galvanometer
Questions Asked in JEE Main exam
- Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $ and $ R $ be a relation on $ A $ defined by $ xRy $ if and only if $ 2x - y \in \{0, 1\} $. Let $ l $ be the number of elements in $ R $. Let $ m $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to:
- JEE Main - 2025
- Relations
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word "MATHS" such that any letter that appears in the word must appear at least twice is:
- JEE Main - 2025
- Calculus
For \( \alpha, \beta, \gamma \in \mathbb{R} \), if \[ \lim_{x \to 0} \frac{x^2 \sin(\alpha x) + (\gamma - 1)e^{x^2}}{\sin(2x - \beta x)} = 3, \] then \( \beta + \gamma - \alpha \) is equal to:
- In \( I(m, n) = \int_0^1 x^{m-1} (1-x)^{n-1} \, dx \), where \( m, n > 0 \), then \( I(9, 14) + I(10, 13) \) is:
- JEE Main - 2025
- Functions
In the first configuration (1) as shown in the figure, four identical charges \( q_0 \) are kept at the corners A, B, C and D of square of side length \( a \). In the second configuration (2), the same charges are shifted to mid points C, E, H, and F of the square. If \( K = \frac{1}{4\pi \epsilon_0} \), the difference between the potential energies of configuration (2) and (1) is given by:
- JEE Main - 2025
- Electromagnetic Field (EMF)