Part of ES-02 — Current Electricity

Reasoning Chain — Why Potentiometer Measures True EMF

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Step 1 — Define the problem: We want to measure the EMF (ε) of a cell. A voltmeter is always connected in parallel — it draws some current.

Step 2 — Why voltmeter fails for true EMF: When voltmeter draws current I, the cell has an internal voltage drop Ir. Voltmeter reads V = ε − Ir, which is LESS than ε. Even a high-resistance voltmeter draws some current.

Step 3 — Potentiometer setup: A uniform wire (A to B) carries a constant current from the driver cell. This sets up a uniform potential gradient k = VwireL\frac{V_wire}{L} V/m along the wire.

Step 4 — Connecting the test cell: The test cell is connected with its positive terminal at A, in opposition to the potential along the wire.

Step 5 — Finding the null point: A jockey slides along the wire. At some position J (distance l from A), the potential at J exactly equals the EMF of the test cell. At this point, the galvanometer reads zero.

Step 6 — Why zero current means true EMF: At the null point, no current flows through the test cell. With I = 0: VterminalV_{terminal} = ε − Ir = ε − 0 = ε. So the potential matched at the null point IS the true EMF.

Step 7 — Quantitative result: ε = kl, where k is the potential gradient Vm\frac{V}{m} and l is the balance length (m). The potential gradient k is calibrated using a known standard cell.

Step 8 — Practical implications: This null method requires no current from the test cell, making it ideal for measuring EMF of cells with internal resistance. The standard cell (1.018 V) provides absolute calibration.

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