A potentiometer wire of length 100\text{ cm} has a resistance of 10\text{ }\Omega. It is c… — JAMB UTME

A potentiometer wire of length $100\text{ cm}$ has a resistance of $10\text{ }\Omega$ . It is connected in series with a driver cell of electromotive force $3.0\text{ V}$ and internal resistance $2.0\text{ }\Omega$ , alongside an external series resistor of $8.0\text{ }\Omega$ . A test cell of unknown electromotive force $E$ gives a balance point at a length of $60\text{ cm}$ from the zero end of the wire. What is the value of $E$ in volts?

Answer: 0.9 V

Answer

The electromotive force of the test cell is

0.9\text{ V}

The e.m.f. of the test cell is balanced by the potential difference across a length of

60\text{ cm}

of the potentiometer wire. Accounting for the driver cell's internal resistance (

2.0\text{ }\Omega

), external series resistor (

8.0\text{ }\Omega

), and wire resistance (

10\text{ }\Omega

), the total resistance of the primary circuit is

20.0\text{ }\Omega

. This yields a primary current of

0.15\text{ A}

and a potential drop across the wire of

1.5\text{ V}

. The resulting potential gradient is

0.015\text{ V/cm}

, which when multiplied by the balance length of

60\text{ cm}

gives an e.m.f. of

0.9\text{ V}

Step-by-Step Solution

Calculate total resistance in the primary driver circuit

R_{total} = 10\text{ }\Omega + 2.0\text{ }\Omega + 8.0\text{ }\Omega = 20.0\text{ }\Omega

The driver cell's internal resistance, potentiometer wire, and external series resistor are connected in series.

Calculate the current flowing through the potentiometer wire

I = \frac{3.0\text{ V}}{20.0\text{ }\Omega} = 0.15\text{ A}

Apply Ohm's law to the complete primary circuit.

Find the voltage drop across the potentiometer wire

V_{wire} = 0.15\text{ A} \times 10\text{ }\Omega = 1.5\text{ V}

The potential difference across the wire depends on its resistance and the primary current.

Determine the potential gradient along the wire

k = \frac{1.5\text{ V}}{100\text{ cm}} = 0.015\text{ V/cm}

Potential gradient is the potential drop per unit length of the wire.

Calculate the e.m.f. of the unknown test cell

E = 0.015\text{ V/cm} \times 60\text{ cm} = 0.9\text{ V}

At the balance point, no current flows from the test cell, so its e.m.f. equals the potential drop across the balance length.

Key Concept

Potentiometer principle and potential gradient

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic