Animated Solution for Physics - Current Electricity: To verify Ohm's law, a student is provided with a test resistor $R_T$, a high resistance $R_1$, a small resistance $R_2$, two identical galvanometers $G_1$ and $G_2$, and a variable voltage source $V$. The correct circuit to carry out the experiment is

The Art of Building Voltmeters and Ammeters

Verifying Ohm's law is a fundamental rite of passage in physics. It requires us to measure two critical quantities simultaneously: the voltage across a test resistor $R_T$ and the current flowing through it. But what if you are only given two identical galvanometers, $G_1$ and $G_2$, along with a high resistance $R_1$ and a low resistance $R_2$? You have to build your own measuring instruments!

A galvanometer is a highly sensitive device that measures tiny currents. To use it to measure voltage across a component, we must connect it in parallel with that component. However, if the galvanometer's resistance is low, it will draw a significant amount of current away from the main circuit, completely altering the voltage we are trying to measure.

To prevent this, we connect a high resistance in series with the galvanometer. This ensures the voltmeter draws negligible current. In our setup, we pair the galvanometer $G_1$ with the high resistance $R_1$ in series to form our voltmeter.

To measure the total current flowing through the test resistor, we need an ammeter connected in series with the circuit. If the ammeter has a high resistance, it will impede the flow of current, changing the very quantity it is supposed to measure.

To solve this, we connect a very low resistance, known as a shunt, in parallel with the galvanometer. This provides an easy bypass for the majority of the current, keeping the total resistance of the ammeter extremely low. We pair the galvanometer $G_2$ with the low resistance $R_2$ in parallel to form our ammeter.

Now that we have our instruments, we must place them correctly in the circuit.

1. The voltmeter ($G_1$ in series with $R_1$) must be connected in parallel with the test resistor $R_T$ to measure the potential difference across it. 2. The ammeter ($G_2$ in parallel with $R_2$) must be connected in series with the circuit to measure the total current.

When we examine the given options, Option (c) perfectly matches this configuration. It shows $G_1$ and $R_1$ in series, acting as the voltmeter in parallel with $R_T$. It also shows $G_2$ and $R_2$ in parallel, acting as the ammeter in series with the rest of the circuit. This is the ideal setup to accurately verify Ohm's law.