Question

Compare the e.m.f. of two given cells with the help of potentiometer.

Hint:

For the experiment to work, the e.m.f. of the driver cell must be greater than the e.m.f. of both cells being compared. Also, ensure all positive terminals are connected to one common point (the high potential end of the potentiometer). Do not slide the jockey along the wire, as it can scrape it and alter its uniformity; tap it gently at different points.

Answer 1

Step 1: Understanding the Concept:
A potentiometer is a device used for accurately measuring potential differences. It operates on the principle that the potential drop across any length of a uniform wire is directly proportional to that length when a constant current flows through it. By balancing the e.m.f. of a cell against the potential drop across a certain length of the potentiometer wire, we can find a "balancing length". By comparing the balancing lengths for two different cells, we can compare their e.m.f.s.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A potentiometer, a driver cell (battery), two primary cells whose e.m.f.s are to be compared (\(\epsilon_1, \epsilon_2\)), a two-way key, a galvanometer, a rheostat, a one-way key, a jockey, and connecting wires.
Key Formula:
If \(l_1\) is the balancing length for the cell with e.m.f. \(\epsilon_1\) and \(l_2\) is the balancing length for the cell with e.m.f. \(\epsilon_2\), then according to the potentiometer principle: \[ \epsilon_1 = k l_1 \quad \text{and} \quad \epsilon_2 = k l_2 \] where k is the potential gradient. The ratio of the e.m.f.s is therefore: \[ \frac{\epsilon_1}{\epsilon_2} = \frac{l_1}{l_2} \] Step 3: Detailed Procedure:
1. Primary Circuit Setup: Connect the driver cell, rheostat, and a one-way key (\(K_1\)) in series with the potentiometer wire.
2. Secondary Circuit Setup: Connect the positive terminals of both given cells (\(\epsilon_1\) and \(\epsilon_2\)) to the high potential end A (the zero end) of the potentiometer. Connect their negative terminals to the terminals 1 and 2 of a two-way key. The common terminal of the two-way key is connected to the jockey through a galvanometer.
3. Finding Balancing Length for \(\epsilon_1\): Close key \(K_1\). Insert the plug into the two-way key to connect cell \(\epsilon_1\) into the circuit. Slide the jockey along the wire to find the null point (where the galvanometer shows zero deflection). Measure the balancing length \(l_1\) from end A.
4. Finding Balancing Length for \(\epsilon_2\): Without changing the rheostat setting, remove the plug for \(\epsilon_1\) and insert it to connect cell \(\epsilon_2\). Find the new null point and measure the balancing length \(l_2\).
Step 4: Calculation:
Calculate the ratio of the e.m.f.s using the measured balancing lengths. \[ \frac{\epsilon_1}{\epsilon_2} = \frac{l_1}{l_2} \] Repeat the experiment by changing the current in the primary circuit using the rheostat and find the mean value of the ratio.