# 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.

Q1:

A 500 Ω resistor, an uncharged 1.50 µF capacitor, and a source with a 6.16 V emf are connected in series.

What is the initial current?

What is the RC time constant?

• A s
• B s
• C s
• D s
• E 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 RC 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 s to 15.0 s?

• A4.33 Ω to 30.0 MΩ
• B4.00 Ω to 30.0 MΩ
• C3.33 Ω to 33.3 MΩ
• D3.00 Ω to 30.0 MΩ
• E4.00 Ω to 40.0 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?

Q5:

An ECG monitor must have an time constant less than 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 F
• B F
• C F
• D F
• E 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 RC time constant?

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

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 capacitor of 10.0 mF, and a power source of 0.500 V to make a circuit.

What is the RC 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 m2, 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

Q17:

In the circuit shown in the diagram, a capacitor can be charged and discharged.

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

• A A
• B A
• C A
• D A
• E A

What is the current through resistor , when the capacitor is fully charged, a long time after the switch is closed?

• A A
• B A
• C A
• D A
• E A

If the switch has been closed for a time interval long enough for the capacitor to become fully charged, and then the switch is opened, how long would it be before the current through resistor reaches half the value it has at the instant that the capacitor starts to discharge?

Q18:

A flashing lamp in a piece of novelty jewelry is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.45 s, during which it produces an average of 0.700 W from an average of 9.0 V potential difference.

How much energy does each flash dissipate?

How much charge moves through the lamp in one flash?

What is the capacitance of the capacitor that stores the charge?

• A F
• B F
• C F
• D F
• E F

What is the resistance of the lamp?

Q19:

Some camera flashes use flash tubes that require a high voltage. They obtain a high voltage by charging capacitors in parallel and then internally changing the connections of the capacitors to place them in series. A circuit uses five 15 V batteries connected in series to charge five 20 mF capacitors through an equivalent resistance of 200 Ω. The connections are then switched internally to place the capacitors in series. The capacitors discharge through a lamp with a resistance of 200 Ω.

What is the RC time constant while the capacitors are connected in parallel?

What is the initial current out of the batteries while the capacitors are connected in parallel?

How long does it take for the capacitors to charge to 80% of the terminal voltages of the batteries?

What is the RC time constant while the capacitors are connected in series?

How long does it take for the current to decrease to 20% of the initial value while discharging?

Q20:

Consider a circuit consisting of a battery with an emf connected in series with a resistor and a capacitor of 500 pF. Find the total energy supplied by the battery while charging it.

• A J
• B J
• C J
• D J
• E J

Q21:

A 3.00 µF capacitor and a 4.50 µF capacitor are connected in parallel and a 12.0 kΩ resistor and a 15.0 kΩ resistor are connected in series. Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.

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