An inductor of inductance 4 H and a resistor are connected in series to a DC battery. The variation of the instantaneous voltage across the inductor ( V_L ) with the instantaneous current ( i ) in the circuit is described by a linear graph. The graph has a y -intercept at V_L = 20 V and an x -intercept at i = 5 A. The rate of change of current at the instant when the current in the circuit is 2 A is

Step-by-step solution

According to Kirchhoff's voltage law for an LR series circuit, the instantaneous voltage across the inductor is given by: V_L = E - iR This represents a linear relationship between V_L and i . The y -intercept (where i = 0 ) gives the EMF of the battery: E = 20 V The x -intercept (where V_L = 0 ) gives the steady-state current: i₀ = E R = 5 A R = 20 5 = 4 , At the instant when the current is i = 2 A, the voltage across the inductor is: V_L = 20 - (2 4) = 20 - 8 = 12 V The rate of change of current is: di dt = V_L L