# Math Help - electricity

1. ## electricity

Here's a question I got for homework and I really do not have a clue on how to do it. Even if somebody could do pieces of it, I would be most grateful.

A capacitor(C) of 10 μF is connected in series with a resistance(R) of 5kΩ across a 20 V
d.c supply (E). Calculate
(i) The initial charging current.
(ii) The initial voltage across the capacitor.
(iii) The Time Constant (T) of the circuit.
(iv) The voltage and current at the Time Constant.
(v) The voltage across the capacitor after 75 milliseconds
(vi) The time for the current to reach 2 mA.
(vii) The time for the voltage to reach 18 V.
(viii) The voltage on the capacitor after a long time period.

Note : The charging current in the circuit is given by i(t) = (E/R) e^-t/CR.

The charging voltage across the capacitor is given by v(t) = E(1- e^-t/CR).

2. Originally Posted by Dean
Here's a question I got for homework and I really do not have a clue on how to do it. Even if somebody could do pieces of it, I would be most grateful.

A capacitor(C) of 10 μF is connected in series with a resistance(R) of 5kΩ across a 20 V
d.c supply (E). Calculate
(i) The initial charging current.
(ii) The initial voltage across the capacitor.
(iii) The Time Constant (T) of the circuit.
(iv) The voltage and current at the Time Constant.
(v) The voltage across the capacitor after 75 milliseconds
(vi) The time for the current to reach 2 mA.
(vii) The time for the voltage to reach 18 V.
(viii) The voltage on the capacitor after a long time period.

Note : The charging current in the circuit is given by i(t) = (E/R) e^-t/CR.

The charging voltage across the capacitor is given by v(t) = E(1- e^-t/CR).

i) $i(t) = (E/R) e^{-t/(CR)}$

$i(0) = (E/R)e^{-0/(CR)} = E/R$

ii) $v(t) = E(1- e^{-t/(CR)})$
Physical intuition should tell you what it ought to be, but you've got the equation here, too.

iii) $T = \frac{1}{CR}$

iv), v) Again, you've got the equations...

vi) Solve $2~mA = (E/R) e^{-t/(CR)}$ for t.

vii) Solve $18~V = E(1- e^{-t/(CR)})$ for t.

viii) Take $\lim_{t \to \infty}v(t) = \lim_{t \to \infty}E(1- e^{-t/(CR)})$

If you have specific questions about any of these I'm glad to help.

-Dan