A 6.50 μF capacitor that is at first uncharged isconnected inseries with a 4500 Ω resistor and also a503 V emf source with negligibleinternal resistance.

You are watching: Just after the circuit is completed, what is the voltage drop across the capacitor?


e)A lengthy time ~ the circuit iscompleted(after countless time constants), what space the worths of theprecedingfour quantities?

The principles used to solve this problem are voltage drop throughout the capacitor, voltage drop across the resistor, charge, and also current in the

*
circuit.

First, usage the ide of charging of a capacitor to discover voltage drop throughout the capacitor and also resistor simply after the circuit is completed.

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

Finally, use the ide of charging the a capacitor to uncover the voltage drop throughout the capacitor, voltage drop across the resistor, charge, and also current a lengthy time after ~ the circuit is completed.


Fundamentals

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

A long time after ~ the circuit is perfect the existing will ideologies zero together the capacitor come to be charged approximately battery voltage.

The expression because that the voltage drop across the capacitor is,

*

Here,

*
is the voltage drop across the capacitor,
*
is the charge, and also
*
is the capacitance.

“The ohm’s legislation states the the potential difference throughout the conductor is proportional come the current.”

The expression because that the voltage is,

*

Here,

*
is the current,
*
is the voltage, and also
*
is the resistance.


(a)

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

The expression because that the voltage drop across the capacitor is,

*

Substitute

*
for
*
.

*

Therefore, the voltage drop across the capacitor is

*
.

(b)

The voltage drop throughout 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 perfect the circuit the fee on the key of the capacitor will be zero.

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

Therefore, the charge on the capacitor just after the circuit is perfect is

*
.

(d)

The expression because that the voltage is,

*

Rearrange the above expression because that

*
.

*

Substitute

*
for
*
and also
*
for
*
.

*

Therefore, the current through the resistor is

*
.

(e)

A lengthy time after ~ the circuit is completed the current will viewpoints zero as the capacitor come to be charged approximately battery voltage.

The voltage drop across the capacitor is

*
.

The voltage drop across the resistor is

*
.

The present through the resistor is zero since the potential drop throughout the resistor is zero.

Current with the resistor is

*
.

The expression for the voltage drop across the capacitor is,

*

Rearrange the over expression because that

*
.

*

Substitute

*
because that
*
and
*
for
*
.

See more: 44 The Man In The High Castle Wallpaper S, The Man In The High Castle Hd Wallpapers

*

The fee on the capacitor is

*
.

Therefore, the voltage drop throughout the capacitor, voltage drop throughout the resistor, charge, and also current a lengthy time after the circuit is perfect is