A moving coil galvanometer has resistance 50 ohm and it indicates full deflection at 4 mA current. A

Q: Why do we connect a high resistance in series to make a voltmeter?

A voltmeter is connected in parallel across the component whose voltage is to be measured. To ensure it doesn't draw significant current and alter the actual voltage of the circuit, its overall resistance must be very high.

Q: What happens if we connect a low resistance instead?

If a low resistance is connected, the voltmeter will draw a large current from the main circuit, significantly dropping the voltage it is supposed to measure, leading to inaccurate readings. It might also damage the galvanometer.

Q: Why did we approximate 20.2 V to 20 V?

In multiple-choice questions, especially in competitive exams like JEE, options are sometimes rounded off. 20.2 V is closest to 20 V among the given choices.

Q: What is 'full scale deflection current'?

It is the maximum current that can safely pass through the galvanometer coil, causing the pointer to move to the extreme end of the scale.

Q: Can we use this voltmeter to measure currents?

No, a voltmeter is designed to measure potential difference. To measure current, you would need an ammeter, which is created by connecting a very low resistance (shunt) in parallel with the galvanometer.

Question

A moving coil galvanometer has resistance $50\ \Omega$ and it indicates full deflection at $4\ 	ext{mA}$ current. A voltmeter is made using this galvanometer and a $5\ 	ext{k}\Omega$ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to

Options:

(A) $40\ 	ext{V}$

(B) $10\ 	ext{V}$

(C) $15\ 	ext{V}$

(D) $20\ 	ext{V}$

Sigma Percentile · Accepted Answer

### The Anatomy of a Voltmeter

Imagine you are holding a delicate moving coil galvanometer. It is a highly sensitive instrument designed to detect even the faintest trickle of electric current. However, if you were to connect it directly across a high-voltage source, the massive surge of current would instantly fry its delicate coil.

So, how do we transform this fragile current-detector into a robust voltage-measuring device? The secret lies in **resistance**.

By connecting a very high resistance in series with the galvanometer, we restrict the flow of current. This combination of a galvanometer and a high series resistance is exactly what constitutes a standard voltmeter. The high resistance ensures that when the voltmeter is connected in parallel across a circuit component, it draws a negligible amount of current, thereby not altering the actual voltage it is trying to measure.

### The Master Equation

According to Ohm's Law, the potential difference $V$ across this entire series combination is simply the product of the current flowing through it and its total resistance.

The maximum voltage this setup can safely measure corresponds to the maximum safe current the galvanometer can handle, known as the full-scale deflection current, denoted by $I_g$.

$$V = I_g (R_g + R)$$

Here, $R_g$ is the internal resistance of the galvanometer, and $R$ is the external high resistance connected in series.

### Executing the Calculation

Let's carefully extract the values given in our problem:
- Full-scale deflection current, $I_g = 4\ 	ext{mA} = 4 	imes 10^{-3}\ 	ext{A}$
- Galvanometer resistance, $R_g = 50\ \Omega$
- Series resistance, $R = 5\ 	ext{k}\Omega = 5000\ \Omega$

First, we determine the total resistance of our newly minted voltmeter:

$$R_{	ext{total}} = R_g + R = 50 + 5000 = 5050\ \Omega$$

Now, we substitute this back into our master equation to find the maximum measurable voltage:

$$V = (4 	imes 10^{-3}\ 	ext{A}) 	imes (5050\ \Omega)$$

$$V = 20200 	imes 10^{-3}\ 	ext{V}$$

$$V = 20.2\ 	ext{V}$$

### The Final Verdict

The theoretical maximum voltage our voltmeter can measure is exactly $20.2\ 	ext{V}$. When we look at the given options, we must select the closest approximate value.

Therefore, the maximum voltage is close to **$20\ 	ext{V}$**, making option (d) the correct choice.

Select Answer:

Visualized Solution

Voltmeter Circuit

Voltage Formula

Substitution

Total Resistance

Calculate Voltage

Final Answer

The Sigma Insight: Moving Coil Galvanometer

The Anatomy of a Voltmeter

The Master Equation

Executing the Calculation

The Final Verdict

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