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Capacitor problems

Capacitor problems. A 470 F capacitor is charged by a 20V cell and then discharged across a 530  resistor. Draw a suitable circuit to achieve this. Show that the time constant for the discharge circuit is 0.25 s. Show that the units of the time constant are seconds (s).

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Capacitor problems

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  1. Capacitor problems

  2. A 470 F capacitor is charged by a 20V cell and then discharged across a 530  resistor. • Draw a suitable circuit to achieve this. • Show that the time constant for the discharge circuit is 0.25 s. • Show that the units of the time constant are seconds (s). • Show that the p.d. across the capacitor has fallen to 7.4 V after 0.25 s. • Plot a graph to show the p.d. across the capacitor after 0.25, 0.50 and 0.75 s.

  3. Answers: • Suitable circuit to include cell, capacitor, 2-way switch, Voltmeter across the capacitor. • Time constant = RC = 530 x 470 x 10-6 = 0.249 s. • Use Q/Qo = e-t/RC to show RC is in s. • After one “RC”, p.d. has dropped by e: 20/e = 20/2.7 = 7.4V • After 0.50 s, V= 7.4/e = 2.7 V. After 0.75 s,V = 2.7/e = 1.0 V. Plot suitable graph.

  4. 2. Use the circuit below for this question: Cell: 6.0V Capacitor: 4700 F Resistor: 5.6 k  A B • When the switch is moved from A to B, what will happen to the capacitor current? • Show the initial value of the current is about 1mA. • What is the time constant of the circuit? • What is the current flowing in the circuit after the switch has been closed for a time equivalent to 2 x RC.

  5. Answers: a) The current will move in the opposite direction to the charging current, and through the resistor as the capacitor DISCHARGES. b) Since I =V/R, I is 6/5600 = 1.1 x 10-3 A c) Time constant = RC = 4700 x 10-6 x 5.6 x 103 = 26.3 s. d) After 2 x RC seconds, I will be 1.1mA/e2 = 1.1/7.29 = 0.15 mA.

  6. 3. A capacitor is used to make a light flash on and off at regular intervals. The capacitor is marked 4700 F and is attached to a 100 V cell and a resistor. • Find the charge on the capacitor. • If the time constant of the circuit is 0.70s, what is the value of the resistor in the circuit? • When the capacitor charges and reaches 72V, the lamp switches on. What is the energy stored in the capacitor? • When the lamp flashes, it transfers energy at an average rate of 150 W.What is the duration of the flash? • Draw a suitable circuit to show how the lamp can be switched on and off. Include all components.

  7. Answers: • Q = CV = 4700 x 10-6 x 100 = 0.47 C • 0.70 = 4700 x 10-6 x R. So R = 150  • E = ½ CV2 = ½ x 4700 x 10-6 x 72 x 72 = 12.2 J • t = 12.2/150 = 0.08 s • Suitable circuit includes capacitor and lamp in parallel with R, switch and cell in series.

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