Use the relationships between capacitor characteristics, complete circuits, and transient charging equations to perform calculations involving charge moved and energy stored in a capacitor in series with a resistor.
A 16 Volt Voltage Source charges up a capacitor when a switch is closed to complete the circuit as shown below. The resistor is 4.5 kΩ and the capacitor is 2000 µf. 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:
Q(t)=Qmax*(1-e-t/RC)
I(t)=Imax*e-t/RC
V(t)=Vmax*(1-e-t/RC)
After the capacitor is fully charged what is the amount of charge contained in the capacitor?
Charge
µC
When the switch is closed what is the initial current in the circuit?
Initial Current
milliAmps
After the capacitor is fully charged what is the current in the circuit?
Current
After the capacitor is fully charged what is the voltage drop across the capacitor?
Voltage
Volts
What is the time constant of this RC circuit?
Time Constant
seconds
How much total energy is stored in the fully charged capacitor?
Total Energy
milliJoules
How much charge is contained in the capacitor 19.35 seconds after closing the switch?
What is the voltage drop across the capacitor 19.35 seconds after closing the switch?
What is the current in the circuit 19.35 seconds after closing the switch?
How much energy is stored in the capacitor 19.35 seconds after closing the switch?
Energy
A Voltage Source charges up a 1700 µf capacitor when a switch is closed to complete the circuit as shown below. The time constant for the circuit is 15.3 seconds and 34000 µC of charge is contained in the capacitor after being fully charged. 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 resistor in the circuit?
Resistance
kΩ
What is the value of the Voltage Source?
Voltage Source
How much energy is stored in the fully charged capacitor?
How much charge is contained in the capacitor 26.775 seconds after closing the switch?
What is the voltage drop across the capacitor 26.775 seconds after closing the switch?
What is the current in the circuit 26.775 seconds after closing the switch?
How much energy is stored in the capacitor 26.775 seconds after closing the switch?
A Voltage Source charges up a 1400 µf capacitor when a switch is closed to complete the circuit as shown below. The initial current in the circuit is 13.333 milliAmps and the total energy stored in the capacitor after being fully charged is 280.0 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:
After the capacitor is fully charged how much charge is contained in the capacitor?
Total Charge
How much charge is contained in the capacitor 3.78 seconds after closing the switch?
What is the voltage drop across the capacitor 3.78 seconds after closing the switch?
What is the current in the circuit 3.78 seconds after closing the switch?
How much energy is stored in the capacitor 3.78 seconds after closing the switch?
A Voltage Source charges up a capacitor when a switch is closed to complete the circuit as shown below. The initial current in the circuit is 8 milliAmps and the voltage drop across the capacitor after being fully charged is 16 Volts. The time constant of this RC circuit is 3.8 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
After the capacitor is fully charged how much energy is stored in the capacitor?
How much charge is contained in the capacitor 7.98 seconds after closing the switch?
What is the voltage drop across the capacitor 7.98 seconds after closing the switch?
What is the current in the circuit 7.98 seconds after closing the switch?
How much energy is stored in the capacitor 7.98 seconds after closing the switch?
A Voltage Source charges up a capacitor when a switch is closed to complete the circuit as shown below. The initial current in the circuit is 4.889 milliAmps and the time constant for this RC circuit is 4.95 seconds. A voltmeter measures the voltage across the capacitor to be 19.562 Volts at 10.89 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 charge is contained in the capacitor 10.89 seconds after closing the switch?
What is the current in the circuit 10.89 seconds after closing the switch?
How much energy is stored in the capacitor 10.89 seconds after closing the switch?
A 12 Volt Voltage Source charges up a capacitor when a switch is closed to complete the circuit as shown below. The time constant for this RC circuit is 6.05 seconds and the charge contained in the capacitor after being fully charged is 13200 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 initial current in the circuit?
At a certain point in time during charging an ammeter measured a current of 0.066 milliAmps in the circuit. How long after the switch was closed was this reading taken?
Time after Switch Closing
What was the voltage drop across the capacitor at the time the 0.066 milliAmps was measured?
What amount of charge was contained in the capacitor at the time the 0.066 milliAmps was measured?
How much energy was stored in the capacitor at the time the 0.066 milliAmps was measured?