Question

A 6.50 μF capacitor that is initially uncharged isconnected in series with a 4500 Ω resistor and a503 V emf source with negligible internal resistance.

a)Just after the circuit is completed, what is the voltagedrop across the capacitor?

                  Vc=                  V

b)Just after the circuit is completed, what is the voltagedrop across the resistor?

                      VR =                 V

c)Just after the circuit is completed, whatis the charge on the capacitor?

                Qo=                     C

d)Just after the circuit is completed, whatis the current through the resistor?

               IR=                 A

e)A long time after the circuit is completed(after many time constants), what are the values of the precedingfour quantities?

          Vc, V R, I,Q=                                  V, V, A, C

Answer 1

Concepts and reason

The concepts used to solve this problem are voltage drop across the capacitor, voltage drop across the resistor, charge, and current in the circuit.

First, use the concept of charging of a capacitor to find voltage drop across the capacitor and resistor just after the circuit is completed.

Then use the relation between current, voltage, and resistance to find the current through the resistor just after the circuit is completed.

Finally, use the concept of charging of a capacitor to find the voltage drop across the capacitor, voltage drop across the resistor, charge, and current a long time after the circuit is completed.

Fundamentals

Just after completing the circuit the charge on the plates of the capacitor will be zero.

A long time after the circuit is completed the current will approaches zero as the capacitor become charged up to battery voltage.

The expression for the voltage drop across the capacitor is,

Here, is the voltage drop across the capacitor, is the charge, and is the capacitance.

“The ohm’s law states that the potential difference across the conductor is proportional to the current.”

The expression for the voltage is,

Here, is the current, is the voltage, and is the resistance.

(a)

Just after completing the circuit the charge on the plates of the capacitor will be zero.

The expression for the voltage drop across the capacitor is,

Substitute for .

Therefore, the voltage drop across the capacitor is .

(b)

The voltage drop across the capacitor is .

All the voltage in the source will drop across the resistor.

Therefore, the voltage drop across the resistor is .

(c)

Just after completing the circuit the charge on the plates of the capacitor will be zero.

When a battery is connected to series resistor and capacitor the charge in the capacitor initially will be zero and current will be high.

Therefore, the charge on the capacitor just after the circuit is completed is .

(d)

The expression for the voltage is,

Rearrange the above expression for .

Substitute for and for .

Therefore, the current through the resistor is .

(e)

A long time after the circuit is completed the current will approaches zero as the capacitor become charged up to battery voltage.

The voltage drop across the capacitor is .

The voltage drop across the resistor is .

The current through the resistor is zero because the potential drop across the resistor is zero.

Current through the resistor is .

The expression for the voltage drop across the capacitor is,

Rearrange the above expression for .

Substitute for and for .

The charge on the capacitor is .

Therefore, the voltage drop across the capacitor, voltage drop across the resistor, charge, and current a long time after the circuit is completed is

.

Ans: Part a

Across the capacitor the voltage drop is .

Part b

Across the resistor the voltage drop is .

Part c

The charge on the capacitor just after the circuit completed is .

Part d

The current through the resistor just after the circuit completed is .

Part e

The value of the four quantities is