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Capacitor Question Practice
A2 Physics
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Q1 What is the energy held by a 50 000 mF capacitor charged to 12.0 V?
(2 marks)
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A1 E = ½ CV2 E = ½ × × 10-6 F × (12.0 V)2 (P) = 3.6 J (P)
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Q2 What is the charge held by a
470 mF capacitor charged to a p.d. of 8.5 V? (2 marks)
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A2 Q = CV (P) = 470 x 10-6 F × 8.5 V = 4.0 × 10-3 C (P)
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What is the capacitance of
Q3 A capacitor is connected to a 12V power supply by a reed switch operating at 400 Hz. The ammeter reads 45 mA. What is the capacitance of the capacitor? (2 marks)
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A3 Q = It but f = 1/t so Q = I/f C = Q/V = I ¸ (Vf)
C = A ¸ (400 Hz × 12.0 V) (P) C = 9.38 × 10-6 F = 9.38 mF (P)
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Q4 A 5000 mF capacitor is charged to 12.0 V and discharged through a 2000 W resistor. (a) What is the time constant? (1 mark) (b) What is the voltage after 13 s? (2 marks) (c) What is the half-life of the decay? (2 marks) (d) How long would it take the capacitor to discharge to 2.0 V (3 marks) (8 marks total)
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4a Time constant = RC = 2000 W × 5000 × 10-6 F = 10 s (P)
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4b V = V0 e –t/RC V = 12.0 × e – 13 /10 (P) V = 12.0 × e – 1.3
= 12.0 × 0.273 = 3.3 volts (P)
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4c V = V0 e –t/RC V ¸ V0 = 0.5 = e –t(half)/RC ln(0.5) = - t1/2 /RC
ln2 = t1/2 /RC (P) (The log of a reciprocal is the negative of that for the original number) t1/2 = × RC = × 10 = 6.93 s (P)
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(When you divide two numbers, you subtract their logs)
V = V0 e –t/RC V ¸ V0 = e –t/RC ln V - ln Vo = -t/RC (P) (When you divide two numbers, you subtract their logs) 0.693 – = - t/10 ln2 - ln12 = - t/10 (P) -t/10 = t/10 = 1.792 t = × 10 = 17.9 s (P)
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