# Answer in Electric Circuits for Hillary #159165

Explanations & Calculations

• The charge stored in a capacitor varies overtime under a given voltage.
• That dependence is expressed in the equation

“qquadqquadnbegin{aligned}nsmall Q_{(t)}&= small CVBig[1-e^{-frac{t}{RC}}Big]\n&= small CVbigg[1-frac{1}{e^{frac{t}{RC}}}bigg]nend{aligned}” “scriptsize v= battery,voltage,R=series,resistance”

• According to this charge accumulated by the capacitor increases overtime & the the rate decreases as there exists an inverse exponential relationship.

• @“qquadqquadnbegin{aligned}nsmall t=0&impliessmall Q_0=0\nsmall ttoinfty &impliessmall Q_{infty}= CVnend{aligned}” “scriptsize charge,increases,and,saturates : rate,decreses”

• And at the very beginning, the effective resistance sensed by the circuit is that from the series resistor. Hence the startup current is

“qquadqquadnbegin{aligned}nsmall V&= small iR\nsmall i_0&= small frac{V}{R}nend{aligned}”

• According to the definition of current, it is “small Q=it”. Plugging this into the capacitor’s equation yeilds

• According to this drawn current decreases overtime exponentially.

• When this behavior is sketched, something like the following is given

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