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The switch in the figure (Figure 1) has been in position a for a long time. It is changed to position b at t=0s.
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Part A
What is the charge Q on the capacitor immediately after the switch is moved to position b?
Express your answer using two significant figures.
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| Q = | Â | Â Â ?CÂ Â |
Part B
What is the current I through the resistor immediately after the switch is moved to position b?
Express your answer using two significant figures.
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| I = | Â | Â Â mAÂ Â |
Part C
What is the charge Q on the capacitor at t=50?s?
Express your answer using two significant figures.
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| Q = | Â | Â Â ?CÂ Â |
Part D
What is the current I through the resistor at t=50?s?
Express your answer using two significant figures.
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| I = | Â | Â Â mAÂ Â |
Part E
What is the charge Q on the capacitor at t=200?s?
Express your answer using two significant figures.
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| Q = | Â | Â Â ?CÂ Â |
Part F
What is the current I through the resistor at t=200?s?
Express your answer using two significant figures.
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| I = | Â | Â Â mA |
A capacitor is composed of 2 plates, a positive and one that is negative. When electrical current moves throughout the electric circuit the capacitor absorbs energy on it’s positive plate. Equal amounts of charge is transferred to the negative plate at the same time and maintains equal charges on both plates. The capacitor is able to store the energy collected in the event that the electrical circuit was shut off.
This problem can be solved by charging an RC circuit.
The charge on a capacitor can initially be calculated by multiplying its capacitance and the voltage of a battery. Ohm’s law later allows you to calculate the current flowing through the circuit. The instantaneous charge of the capacitor can then be calculated by multiplying the instantaneous voltage with the capacitance.
The ratio of the instantaneous resistance to the voltage can then be used to calculate the instantaneous charge. The instantaneous charge of the capacitor can also be calculated by multiplying the instantaneous voltage with the capacitance. The ratio of the instantaneous resistance and the voltage can be used to calculate the instantaneous charge.
Below is the expression for the charge of the capacitor:
This is the expression of the current within the circuit:
Below is the expression for the instantaneous voltage:
This is the expression of the instantaneous capacitor charge:
Below is the expression for the instantaneous current:
(A)
This is the expression for the charge on a capacitor:
Substitute 2 μF to C and 9 V to V
(B)
This is the expression for current:
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, -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
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.
(c)
This is the expression for instantaneous voltage:
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to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
; -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
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to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
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respectively for -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
.
Below is the expression for an instantaneous cost.
Substitute 5.459 V to-has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
and 2 μF to C.
(d)
This is the expression for instantaneous current:
Substitute 5.459 V to-has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
or 50 Ω to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
.
(e)
This is the expression for instantaneous voltage:
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to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
; -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
; -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
; -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
; -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
-has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
; -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
-has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
Below is the expression for an instantaneous cost.
Substitute 1.218 VÂ to-has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
or 2.0 μF to -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
.
(f)
This is the expression for instantaneous current:
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, -has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)
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Ans Part A
The charge on a capacitor is-has-been-in-position-a-for-a-long-time.-It-is-changed-to-position-b-at-t=0s.-Par.png?x-oss-process=image/resize,w_560/format,webp)