# Worksheet: Capacitor Charging and Discharging

In this worksheet, we will practice describing exponential changes with time in capacitive circuits, knowing that such changes depend on a circuit's time constant.

**Q2: **

The timing device in an automobile’s intermittent wiper system is based on an time constant and utilizes a 0.500-μF capacitor and a variable resistor. Over what range must 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 RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a 600- capacitor, what is the resistance in the flash tube?

- A Ω
- B Ω
- C Ω
- D Ω
- E Ω

**Q4: **

The duration of a photographic flash is related to an 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?

**Q7: **

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 . Assume that all of the thermal energy resulting from the discharge is retained in the short time that the discharge lasts.

**Q8: **

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

What is the energy stored in ?

What is the energy stored in ?

**Q9: **

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?

**Q10: **

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 . 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 time constant of the circuit?

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

**Q11: **

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 ?

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

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

**Q12: **

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

**Q13: **

A heart pacemaker generates electrical pulses 60 times a minute. A battery in series with a resistor charges the pacemaker’s 40 nF capacitor to 0.630 of the capacitor’s full voltage with each pulse. What is the resistance of the resistor?

**Q14: **

A circuit contains a D cell battery, a switch, a 30 Ω resistor, and three 40 mF capacitors. The capacitors are connected in parallel, and the parallel connection of capacitors is connected in series with the switch, the resistor, and the battery.

What is the equivalent capacitance of the circuit?

What is the RC time constant?

How long would it be before the current decreases to 50% of the initial value once the switch is closed?

**Q15: **

A homemade capacitor is constructed of two sheets of aluminum foil each with an area of 3.00 m^{2}, separated by 0.10 m
of paper that has a dielectric constant of 2.9. The homemade capacitor is connected in series with a 200 Ω resistor, a switch, and a 9.00 V
voltage source.

What is the RC time constant of the circuit?

- A s
- B s
- C s
- D s
- E s

What is the initial current through the circuit when the switch is closed?

How long does it take the current to reach one-third of its initial value?

- A s
- B s
- C s
- D s
- E s

**Q16: **

A heart defibrillator being used on a patient has an RC time constant of 8.0 ms due to the resistance of the patient and the capacitance of the defibrillator.

The defibrillator has a capacitance of 9.00 µF. Find the resistance of the path that the defibrillation current takes through the patient, neglecting the capacitance of the patient and the resistance of the defibrillator.

- A Ω
- B Ω
- C Ω
- D Ω
- E Ω

If the initial voltage of the defibrillator is 9.0 kV, how long does it take for this voltage to decline to 0.40 kV?

- A s
- B s
- C s
- D s
- E s