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EMF and internal resistance questions
Every real cell resists the charge passing through its own chemicals, and that internal resistance is why the pd a circuit receives sags below the cell's emf as the current grows. Plotting terminal potential difference against current gives a near-straight line whose intercept is the emf and whose gradient is the internal resistance.
19 original questions · 58 marks · the emf and internal resistance notes · Electricity
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Define the electromotive force (emf) of a source.
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The emf is the energy transferred to each unit of charge by the source, ε = W/Q (1). It is measured in volts, or joules per coulomb (1).A battery of emf 6.0 V and internal resistance 1.0 Ω supplies a current of 0.50 A. Calculate its terminal potential difference.
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V = ε − Ir = 6.0 − 0.50 × 1.0 (1)
V = 5.5 V (1)State the equation linking emf, current, external resistance and internal resistance.
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ε = I(R + r) (1), where R is the external resistance and r the internal resistance (1).State the condition under which the terminal pd of a cell equals its emf.
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When no current flows (I = 0), since the lost volts Ir are then zero (1).A battery of emf 9.0 V has a terminal pd of 8.4 V while supplying a current. Calculate the lost volts, and state where the corresponding energy is transferred.
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Lost volts = ε − V = 9.0 − 8.4 = 0.6 V (1); the energy is dissipated in the internal resistance, warming the battery (1).Explain why a digital voltmeter of very high resistance connected directly across an isolated cell reads almost exactly the cell's emf.
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The voltmeter draws almost no current from the cell (1), so the lost volts Ir are negligible and the terminal pd is (almost) equal to ε (1).A cell of emf 12 V and internal resistance 1.0 Ω is connected to an external resistor of 5.0 Ω. Calculate the current in the circuit.
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I = ε/(R + r) (1)
I = 12/(5.0 + 1.0) (1)
I = 2.0 A (1)A battery of emf 9.0 V and internal resistance 0.50 Ω is connected to a 4.0 Ω resistor. Calculate (a) the current, (b) the terminal potential difference and (c) the power dissipated inside the battery.
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(a) I = 9.0/(4.0 + 0.50) = 2.0 A (1)
(b) V = IR = 2.0 × 4.0 (1)
V = 8.0 V (1)
(c) Pinternal = I2r = 2.02 × 0.50 = 2.0 W (1)A cell of emf 1.5 V delivers a current of 0.30 A, and its terminal potential difference falls to 1.35 V. Calculate the internal resistance of the cell.
A cell of emf 6.0 V has an internal resistance of 0.20 Ω. Calculate the current if its terminals are short-circuited (R = 0).
A battery has a terminal pd of 5.7 V when supplying a current of 0.60 A, and 5.1 V when supplying 1.8 A. Determine the internal resistance and the emf of the battery.
A car battery of emf 12.6 V and internal resistance 25 mΩ supplies 160 A to the starter motor. Calculate the terminal pd of the battery, and determine the fraction of the battery's power that is delivered to the external circuit.
A cell of emf 6.0 V and internal resistance 0.50 Ω is connected to two 5.0 Ω resistors in parallel. Calculate the current supplied by the cell and the cell's terminal pd.
A graph of terminal potential difference V against current I for a cell is a straight line with a V-axis intercept of 1.5 V and a gradient of −0.5 V A−1. State the emf and internal resistance, and calculate the terminal pd when the current is 1.0 A.
A battery of emf 12 V and internal resistance 2.0 Ω is connected to a variable resistor. Calculate the resistance value that makes the terminal potential difference equal to 10 V.
Explain why the terminal potential difference of a battery falls as it supplies a larger current.
Describe an experiment to determine the emf and internal resistance of a cell using a variable resistor, an ammeter and a voltmeter. Explain how the results are processed, and why this method gives a better value for the emf than a single voltmeter reading across the cell.
A model boat's motor needs a pd of at least 4.4 V across it while drawing 2.0 A. Two batteries are available: battery P (emf 6.0 V, internal resistance 0.90 Ω) and battery Q (emf 5.0 V, internal resistance 0.20 Ω). Deduce which battery should be used.
Two identical cells, each of emf 1.5 V and internal resistance 0.30 Ω, are connected in series to a 2.4 Ω resistor. Calculate the current in the circuit and the pd across the resistor.
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