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Worksheet: Capacitor Charging and Discharging

Q1:

A 500- Ω resistor, an uncharged 1.50- 𝜇 F capacitor, and a 6.16-V emf are connected in series.

What is the initial current?

What is the 𝑅 𝐶 time constant?

  • A 7 . 5 0 × 1 0 4 s
  • B 1 . 1 0 × 1 0 3 s
  • C 9 . 5 0 × 1 0 4 s
  • D 5 . 0 0 × 1 0 4 s
  • E 1 . 3 0 × 1 0 3 s

What is the current after one time constant?

What is the voltage on the capacitor after one time constant?

Q2:

The timing device in an automobile’s intermittent wiper system is based on an 𝑅 𝐶 time constant and utilizes a 0.500-μF capacitor and a variable resistor. Over what range must 𝑅 be made to vary to achieve time constants from 2.00 to 15.0 s?

  • A4.00 to 40.0 MΩ
  • B3.00 to 30.0 MΩ
  • C3.33 to 33.3 MΩ
  • D4.00 to 30.0 MΩ
  • E4.33 to 30.0 MΩ

Q3:

If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an 𝑅 𝐶 discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one 𝑅 𝐶 constant is acceptable, and given that the flash is driven by a 600- 𝜇 F capacitor, what is the resistance in the flash tube?

  • A 3 . 9 6 × 1 0 3 Ω
  • B 3 . 7 0 × 1 0 3 Ω
  • C 4 . 2 2 × 1 0 3 Ω
  • D 3 . 3 3 × 1 0 3 Ω
  • E 4 . 5 5 × 1 0 3 Ω

Q4:

The duration of a photographic flash is related to an 𝑅 𝐶 time constant, which is 0.100 µs for a certain camera. The capacitor in the camera is in a circuit with a charging resistance of 800 kΩ, while the flash lamp of the camera has a resistance of 40.0 mΩ during discharge.

What is the capacitance of the capacitor?

What is the time constant for charging the capacitor?

Q5:

An ECG monitor must have an 𝑅 𝐶 time constant less than 1 . 0 0 × 1 0 µs to be able to measure variations in voltage over small time intervals. If the resistance of the circuit (due mostly to that of the patient’s chest) is 1.00 kΩ, what is the maximum capacitance of the circuit?

  • A 1 . 2 2 × 1 0 F
  • B 1 . 1 5 × 1 0 F
  • C 1 . 3 0 × 1 0 F
  • D 1 . 0 0 × 1 0 F
  • E 1 . 4 1 × 1 0 F

Q6:

A circuit contains a D cell battery, a switch, a 20- Ω resistor, and four 20-mF capacitors connected in series.

What is the equivalent capacitance of the circuit?

What is the 𝑅 𝐶 time constant?

How long before the current decreases to 5 0 % of the initial value once the switch is closed?

Q7:

Consider the circuit shown.

What is the time constant of the circuit?

What is the initial current in the circuit once the switch is closed?

How much time passes between the instant the switch is closed and the time at which the magnitude of the current becomes half that of the magnitude of the current in the circuit just after the switch was closed?

Q8:

A student makes a homemade resistor from a graphite pencil 5.00 cm long, where the graphite is 0.05000 mm in diameter. The graphite has resistivity 𝜌 = 1 . 3 8 × 1 0 / 5 Ω m . The homemade resistor is placed in series with a switch, a 10.0-mF capacitor, and a 0.500-V power source to make a circuit.

What is the 𝑅 𝐶 time constant of the circuit?

What is the potential drop across the pencil 1.00 s after the switch is closed?

Q9:

The capacitors in the network shown are all uncharged when a 240 V potential is applied between points A and B with the switch S open.

What is the potential difference 𝑉 𝑉 E D ?

What is the potential at point E after the switch is closed?

How much charge flows through the switch after it is closed?

Q10:

Consider the circuit shown. Assume that the switch has been closed for a very long time.

What is the energy stored in 𝐶 1 ?

What is the energy stored in 𝐶 2 ?

Q11:

How much time is required to charge an initially uncharged 500 pF capacitor to 9 0 . 0 % of its maximum voltage if a resistance of 65.0 MΩ is included in the charging circuit?

Q12:

A circuit contains a 160 µF capacitor charged to 450 V. The circuit is discharged through a 31.2-kΩ resistor.

Find the time constant of the circuit.

Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat capacity is 1 . 6 7 / k J k g C . Assume that all of the thermal energy resulting from the discharge is retained in the short time that the discharge lasts.