A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistanceof R is 4.0 Ω.VRS 4.0 ΩWhen S is open the reading on the voltmeter is 12 V. When S is closed the voltmeterreads 8.0 V.(i) State the emf of the cell. [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(ii) Deduce the internal resistance of the cell
Question
A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistanceof R is 4.0 Ω.VRS 4.0 ΩWhen S is open the reading on the voltmeter is 12 V. When S is closed the voltmeterreads 8.0 V.(i) State the emf of the cell. [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(ii) Deduce the internal resistance of the cell
Solution
(i) The electromotive force (emf) of the cell is the voltage across the cell when no current is flowing. This is when the switch S is open. Therefore, the emf of the cell is 12 V.
(ii) When the switch S is closed, current flows through the circuit and the voltmeter reads a lower voltage (8.0 V). This is because some of the cell's emf is used to push current through the internal resistance of the cell.
We can use Ohm's law (V = IR) to find the current flowing through the resistor R when the switch is closed. The voltage across R is 8.0 V and the resistance of R is 4.0 Ω, so the current I is 8.0 V / 4.0 Ω = 2.0 A.
The difference between the emf of the cell and the voltage across R when the switch is closed is the voltage across the internal resistance of the cell. This is 12 V - 8.0 V = 4.0 V.
Again using Ohm's law, we can find the internal resistance r of the cell. The voltage across r is 4.0 V and the current I is 2.0 A, so the internal resistance r is 4.0 V / 2.0 A = 2.0 Ω.
Similar Questions
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