Objective

The goal is to set up a circuit to verify Ohm's law, which states that the voltage ($V$) across a resistor is directly proportional to the current ($I$) flowing through it, i.e., $V = IR_T$. To verify this, we need to measure the current flowing through the test resistor $R_T$ and the potential difference (voltage) across it.

Required Instruments and their Construction

1. Ammeter: An ammeter measures current and must be connected in series with the component through which the current is to be measured. An ideal ammeter has zero resistance. A practical ammeter is constructed by connecting a low-resistance shunt ($R_s$) in parallel with a galvanometer (G). This ensures that most of the current passes through the shunt, protecting the galvanometer, and the overall resistance of the ammeter is very low. From the given components, we can construct an ammeter using galvanometer $G_2$ and the small resistance $R_2$ as the shunt. So, the ammeter will be a parallel combination of $G_2$ and $R_2$.

2. Voltmeter: A voltmeter measures potential difference and must be connected in parallel across the component whose voltage is to be measured. An ideal voltmeter has infinite resistance. A practical voltmeter is constructed by connecting a high resistance ($R_{series}$) in series with a galvanometer (G). This high resistance limits the current drawn by the voltmeter from the main circuit, preventing it from significantly altering the circuit's behavior. From the given components, we can construct a voltmeter using galvanometer $G_1$ and the high resistance $R_1$ in series. So, the voltmeter will be a series combination of $G_1$ and $R_1$.

Circuit Assembly

To verify Ohm's law for the test resistor $R_T$:

1. The ammeter (constructed from $G_2$ and $R_2$) should be connected in series with $R_T$ to measure the current $I$ flowing through $R_T$.
2. The voltmeter (constructed from $G_1$ and $R_1$) should be connected in parallel with $R_T$ to measure the voltage $V$ across $R_T$.
3. A variable voltage source $V$ is used to supply power to the circuit and to vary the current and voltage to obtain multiple readings.

Analysis of the Options

Let's examine each of the given circuits:

• Circuit A: It shows $G_1$ in parallel with $R_1$ (high resistance) and $G_2$ in series with $R_2$ (small resistance). This is the incorrect way to construct a voltmeter and an ammeter.

• Circuit B: It shows a correctly constructed voltmeter ($G_1$ in series with $R_1$). However, the ammeter is incorrectly constructed ($G_2$ in series with $R_2$).

• Circuit C:

  • The ammeter part consists of $G_2$ in parallel with the small resistance $R_2$. This is the correct way to construct an ammeter.
  • The voltmeter part consists of $G_1$ in series with the high resistance $R_1$. This is the correct way to construct a voltmeter.
  • The ammeter is connected in series with the test resistor $R_T$.
  • The voltmeter is connected in parallel across the series combination of $R_T$ and the ammeter. Since the ammeter has a very low resistance, the potential drop across it is negligible. Therefore, the voltmeter reading is approximately the potential difference across $R_T$. This is a standard and correct circuit for verifying Ohm's law.

• Circuit D: It shows $G_1$ in series with $R_2$ (small resistance) to act as a voltmeter, and $G_2$ in parallel with $R_1$ (high resistance) to act as an ammeter. Both instruments are incorrectly constructed. A voltmeter needs a high series resistance, and an ammeter needs a low shunt resistance.

Conclusion

Based on the analysis, circuit C is the only one where the ammeter and voltmeter are correctly designed using the given components and are connected properly in the circuit to verify Ohm's law.