The figure shows a circuit containing an electromotive force, acapacitor with a capacitance of C farads (F), and aresistor with a resistance of R ohms (?). The voltage dropacross the capacitor is Q/C, where Q isthe charge (in coulombs, C), so in this case Kirchhoff's Lawgives
RI + Q/C =E(t)
But I = dQ/dt, so we have
R(dQ/dt) + 1/C (Q) = E(t)
Suppose the resistance is 10 ?, the capacitance is 0.05 F, and abattery gives a constant voltage of 60 V.
If the initial charge is Q(0) = 0 C, use Euler's methodwith step size 0.1 to estimate the charge, Q after half asecond. (Round your answer to two decimal places.)
Q(0.5) = ???
