"Determine the electrical resistance of a voltmeter."

Experiment to determine the resistance of a voltmeter by connecting it in series with a resistance box and battery, then plotting a graph between R and 1/V.

Apparatus

Battery
Voltmeter
Resistance box
Key and connecting wires

Theory

We connect a battery of electromotive force $E$ in series with a resistance $R$ from a resistance box (R.B.), a key $K$ , and a voltmeter $V$ . The voltmeter’s resistance $R_V$ is the quantity we aim to determine.

Typically, a voltmeter connects in parallel, but in this experiment, we connect it in series. In this arrangement, the voltmeter measures the potential difference $V$ across its own resistance $R_V$ .

The current $I$ flowing through the circuit is:

$\frac{E}{R + R_V}$

The potential difference across the voltmeter is:

$V = I R_V$

From this relation, we calculate the resistance of the voltmeter as:

$\frac{E R_V – V}{V}$

To find the RVR $R_{V}$ graphically, we plot $R$ versus $1/ V$ . The x-axis intercept of the resulting straight line gives the resistance $R_V$ .

Precautions Before the Experiment

Draw a neat circuit diagram as in Figure 3(a).
Clean all ends of the connecting wires.
Connect the positive terminal of the voltmeter to the battery’s positive pole.
Ensure all connections are tight and secure.
Change the resistance $R$ in equal steps.
Take the graph origin as $(0, 0)$ for accuracy.

Experimental Procedure

Step 1: Setup

Arrange the battery, key, resistance box, and voltmeter in series.

Step 2: Initial Reading

Apply a suitable resistance $R$ from the resistance box and close the key. Record the voltmeter reading $V$ .

Step 3: Vary Resistance

Increase $R$ in equal steps and record at least six voltmeter readings.

Step 4: Calculate 1/V

For each observation, calculate $1/ V$ .

Step 5: Plot Graph

Plot $R$ on the x-axis and $1/ V$ on the y-axis. Extend the straight line to meet the x-axis.

Step 6: Determine Voltmeter Resistance

The x-axis intercept gives the voltmeter’s resistance $R_V$ .

Observations and Calculations

No of obs.	Voltmeter Reading V (volts)	Resistance R (ohms)	(Volt)^-1
1 2 3 4 5 6	0 500 1000 1500 2000 2500	2.6 1.8 1.4 1.1 1.0 0.8	0.38 0.55 0.71 0.90 1.0 1.25

Intercept of the graph on the x-axis: = ______ ohm.

Resistance of the voltmeter: = intercept of the graph

= R_V = 1200 ohms.

Precautions:

All the connections should be clean and tight.
The terminal of the voltmeter marked + should be connected to the positive pole and the other terminal to the negative pole of the battery.
Change the resistance R in equal steps.
The origin of the graph should be taken as (0,0).

Viva Questions and Answers

Basic Concepts

Q1. What is a voltmeter?
A voltmeter measures the potential difference between two points. It consists of a galvanometer in series with a high resistance.

Q2. Why must a voltmeter have high resistance?
High resistance ensures it draws negligible current, so it does not affect the measured potential difference.

Q3. How can a galvanometer convert into a voltmeter?
We connect a suitable high resistance in series with the galvanometer.

Q4. Can an AC voltmeter measure DC voltage?
No, it cannot measure DC voltage accurately.

Units and Definitions

Q5. Define the unit of potential difference.
One volt is the potential difference that moving one coulomb of charge requires one joule of work.

Q6. What is a potential difference?
Potential difference equals the work done in moving a unit positive charge between two points in an electric field.

Circuit Connections

Q7. How is a voltmeter connected in a circuit?
We always connect a voltmeter in parallel across the component whose potential difference we want to measure.

Q8. Why is it connected in parallel?
The voltmeter measures the exact potential difference across the component.

Q9. What is an ideal voltmeter?
An ideal voltmeter has infinite resistance and draws no current.

Q10. Can an ordinary voltmeter measure accurately?
No, it draws some current, slightly affecting the measurement.

Advanced Concepts

Q11. Which instruments measure voltage more accurately?
A cathode ray oscilloscope (CRO) or a digital voltmeter can measure voltage precisely.

Q12. How does potential difference vary across series resistance?
Potential difference increases with resistance since the current remains constant in a series circuit ( $V = I R$ ).

Q13. Which resistance is called low resistance?
Any resistance below one ohm, including fractional values, is considered low.

Q14. How do we calculate the voltmeter resistance from the graph?
It equals the negative x-axis intercept of the straight line between $R$ and $1/ V$ .

Q15. Why change resistance in equal steps?
Equal steps give uniform data and improve graph accuracy.

Q16. Why take the graph origin as (0,0)?
It ensures correct scaling and accurate determination of $R_V$ .

“Determine the electrical resistance of a voltmeter.”