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EMF and internal resistance questions
Every real cell resists its own current, and that hidden resistance is what stands between the voltage on the label and the voltage you get. One straight-line graph exposes both of a cell's secrets at once.
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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