Use the relationships between capacitor characteristics, complete circuits, and transient discharging equations to perform calculations involving charge moved and energy stored in a capacitor in series with a resistor.
A charged 1100 µf capacitor is arranged in an open circuit as shown below. The resistor is 7.0 kΩ and the voltage drop across the capacitor is 18 Volts. The equations that govern the discharge of the capacitor regarding charge contained in the capacitor, current in the circuit, and voltage across the capacitor over time are graphed below right and are as follows:
Q(t)=Qmax*e-t/RC
I(t)=-Imax*e-t/RC ; the - sign before Imax indicates the current when discharging is opposite the direction of current when charging.
V(t)=Vmax*e-t/RC
What is the amount of charge in the capacitor before the switch is closed?
Charge
µC
How much total energy is stored in the charged capacitor before the switch is closed?
Total Energy
milliJoules
When the switch is closed what is the magnitude of the initial current in the circuit?
Initial Current
milliAmps
After the capacitor is fully discharged what is the current in the circuit?
Current
After the capacitor is fully discharged what is the voltage drop across the capacitor?
Voltage
Volts
What is the time constant of this RC circuit?
Time Constant
seconds
How much charge is contained in the capacitor 14.63 seconds after closing the switch?
What is the voltage drop across the capacitor 14.63 seconds after closing the switch?
What is the magnitude of the current in the circuit 14.63 seconds after closing the switch?
How much energy is stored in the capacitor 14.63 seconds after closing the switch?
Energy
A charged 1800 µf capacitor is arranged in an open circuit as shown below. The time constant for the circuit is 16.2 seconds and 28800 µC of charge is contained in the capacitor before the switch is closed. The equations that govern the discharge of the capacitor regarding charge contained in the capacitor, current in the circuit, and voltage across the capacitor over time are graphed below right and are as follows:
What is the value of the resistor in the circuit?
Resistance
kΩ
What is the voltage drop across the capacitor before the switch is closed?
When the switch is closed what is the initial current in the circuit?
How much energy is stored in the fully charged capacitor?
How much charge is contained in the capacitor 45.36 seconds after closing the switch?
What is the voltage drop across the capacitor 45.36 seconds after closing the switch?
What is the magnitude of the current in the circuit 45.36 seconds after closing the switch?
How much energy is stored in the capacitor 45.36 seconds after closing the switch?
A charged 1700 µf capacitor is arranged in an open circuit as shown below. When the switch is closed the magnitude of the initial current in the circuit is 6.857 milliAmps and the total energy stored in the capacitor before the switch is closed is 489.6 milliJoules. The equations that govern charge contained in the capacitor, current in the circuit, and voltage across the capacitor over time are graphed below right and are as follows:
Before the switch is closed what is the voltage drop across the capacitor?
Before the switch is closed how much charge is contained in the capacitor?
How much charge is contained in the capacitor 8.925 seconds after closing the switch?
What is the voltage drop across the capacitor 8.925 seconds after closing the switch?
What is the magnitude of the current in the circuit 8.925 seconds after closing the switch?
How much energy is stored in the capacitor 8.925 seconds after closing the switch?
A charged capacitor is arranged in an open circuit as shown below. When the switch is closed the magnitude of the initial current in the circuit is 2.5 milliAmps, the initial voltage across the capacitor is 20 Volts, and the time constant for this circuit is 12.8 seconds. The equations that govern charge contained in the capacitor, current in the circuit, and voltage across the capacitor over time are graphed below right and are as follows:
What is the value of the capacitor in the circuit?
Capacitance
µf
What is the amount of charge contained in the fully charged capacitor?
How much charge is contained in the capacitor 44.8 seconds after closing the switch?
What is the voltage drop across the capacitor 44.8 seconds after closing the switch?
What is the magnitude of the current in the circuit 44.8 seconds after closing the switch?
How much energy is stored in the capacitor 44.8 seconds after closing the switch?
A charged capacitor is arranged in an open circuit as shown below. The switch is closed causing the capacitor to be discharged. The initial current in the circuit is 1.474 milliAmps and the time constant for this RC circuit is 14.25 seconds. A voltmeter measures the voltage across the capacitor to be 1.802 Volts at 29.213 seconds after closing the switch. The equations that govern charge contained in the capacitor, current in the circuit, and voltage across the capacitor over time are graphed below right and are as follows:
How much energy was stored in the capacitor before the switch was closed?
How much charge is contained in the capacitor 29.213 seconds after closing the switch?
What is the magnitude of the current in the circuit 29.213 seconds after closing the switch?
How much energy is stored in the capacitor 29.213 seconds after closing the switch?
A capacitor is discharged when a switch is closed to complete the circuit as shown below. The time constant for this RC circuit is 14.45 seconds. Before the switch is closed the voltage across the capacitor is 12 Volts and the charge contained in the capacitor is 20400 µC. The equations that govern charge contained in the capacitor, current in the circuit, and voltage across the capacitor over time are graphed below right and are as follows:
After the switch is closed what is the magnitude of the initial current in the circuit?
Before the switch is closed how much energy is stored in the capacitor?
At a certain point in time during charging an ammeter measured a current of -0.064 milliAmps in the circuit. How long after the switch was closed was this reading taken?
time
What was the voltage drop across the capacitor at the time the -0.064 milliAmps was measured?
What amount of charge was contained in the capacitor at the time the -0.064 milliAmps was measured?
How much energy was stored in the capacitor at the time the -0.064 milliAmps was measured?