A resistor (10 Ω) and capacitor (1 F) are linked in series with an electromotive force (se...

A resistor (10 Ω) and capacitor (1 F) are linked in series with an electromotive force (see Figure). Initially, there is no charge on the capacitor. The emf produces a constant voltage difference of 100 V for the first five seconds, after which it is switched off.

(a) Use a numerical solver to approximate the charge on the capacitor at the end of 10 seconds.

(b) Set up and solve a differential equation modeling this circuit, then use the resulting formula to calculate the charge on the capacitor at the end of 10 seconds.

Figure An RC circuit