An uncharged capacitor and a resistor are connected in series to a battery as shown. If $\varepsilon$ = 15 V,C = 20 $\mu$F,and R = 4.0 $\times$ 10⁵ $\Omega$,the current as a function of time for this circuit is A)I(t)= 37.5 e^-0.250^t $\mu$A B)I(t)= 150 e^-0.250^t $\mu$A C)I(t)= 37.5 e^-0.125^t $\mu$A D)I(t)= 300 e^-0.125^t $\mu$A

Question

Quizplus · Accepted Answer

The time constant (τ) for this circuit is

τ = RC = (4.0 x 10^10 Ω) x (20 x 10^-6 F) = 0.8 seconds

The current as a function of time for a charging RC circuit is given by 
I(t) = (ε/R) * (1 - e^(-t/τ))

Plugging in the given values, we get

I(t) = (15 V / 4.0 x 10^10 Ω) * (1 - e^(-t / 0.8 s))
      = 3.75 x 10^-10 * (1 - e^(-1.25t)) A

So the answer is C) I(t) = 37.5 e^(-0.125 t) μF1F1F1S1A.

An Uncharged Capacitor and a Resistor Are Connected in Series ε\varepsilonε

An Uncharged Capacitor and a Resistor Are Connected in Series $\varepsilon$