In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an elect force (see figure 4.9), we are led to an initial value problem of the form where l is the inductance in henrys, r is the resistance in ohms, c is the capacitance in farads, e(t) is the electromotive force in voits, qit) is the charge in coulombs on the capacitor at time t, and i-dg/dt is the current in amperes. find the current at time t if the charge on the capacitor is initially zero, the initial current is zero, l= 10 h, r-20 ω, ca(6260)-1f, and e(t)-100 v. [hint: differentiate both sides of the differential equation in (20) to obtain a homogeneous linear second-order equation for i(t). then use (20) to determine d/dt at t-o.]