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3 years ago

10

A 100-volt electromotive force is applied to an rc-series circuit in which the resistance is 500 ohms and the capacitance is 10?

4 farad. find the charge q(t) on the capacitor if q(0) = 0.'

1 answer:

GarryVolchara [31]3 years ago

5 0

We are given
V = 100 V
R = 500 Ω
C = 10^4 F
q(0) = 0

We are asked to find the charge q(t) of the RC capacitor.

To solve this, we use the formula:
q(t) = CV [1 - e^(-t/RC) ]
Substituting thet given values
q(t) = 10^4 (100) [1 - e^(-t/500(10^4) ]
q(t) = 1 x 20^6 [1 - e^(-2x10^7 t) ]
Since we only asked to get the charge q(t) in terms of t, the answer is
q(t) = 1 x 20^6 [1 - e^(-2x10^7 t) ]

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$\theta = \theta_{o} + \omega_{o}\cdot t + \frac{1}{2}\cdot \alpha \cdot t^{2}$

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$\theta$ - Final angular position, measured in radians.

$\theta_{o}$ - Initial angular position, measured in radians.

$\omega_{o}$ - Initial angular speed, measured in radians per second.

$\alpha$ - Angular acceleration, measured in radians per square second.

$t$ - Time, measured in seconds.

If $\theta_{o} = 0\,rad$ , $\omega_{o} = 0\,\frac{rad}{s}$ , $\alpha = 15\,\frac{rad}{s^{2}}$ , the final angular position is:

$\theta = 0\,rad + \left(0\,\frac{rad}{s}\right)\cdot (2.50\,s) + \frac{1}{2}\cdot \left(15\,\frac{rad}{s^{2}}\right)\cdot (2.50\,s)^{2}$

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$\theta = 7.46\,rev$

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