Consider an RL circuit consisting of an inductor with an inductance of L henry(H)and a resistor with a resistance of Rohms (1) driven by a voltage of E(t) volts (V). Given the voltage drop across the resistor is ER = RI, and across the inductor is E₁ = L(dI / dt), Kirchhoff's Law gives Er(t) Now suppose an RL circuit with a 9 resistor and a 0.02H inductor is driven by a constant voltage of 105V. If the initial resistor current is I(0) = 0A, find the current I and the voltages across the inductor EL and the resistorER in terms of time t. I(t) = EL(t) = dI L +RI= = dt = E(t) A V V

For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

8. The p.d., V, between the plates of a capac- itor C charged by a steady voltage E through a resistor R is given by the equation dV CR +V=E. dt (a) Solve the equation for V given that at t=0, V=0. (b) Calculate V, correct to 3 significant figures, when E=25V, C =20 x10–6F, R=200 ×10³ 2 and t=3.0 s.

Suppose f = f(g, h), g = g(t), and h = h(t). Find df/dt when t = 2, given the following. g(2) = -9, g'(2) = 7, h(2) = 8, h'(2) = 9, fg(-9, 8) = 5, and fh(-9, 8) = 3,