To apply problem solving strategy 212 Inductors in circuits

To apply problem solving strategy 21.2 Inductors in circuits. Consider the circuit in the diagram, containing two identical resistors, R_A and R_B, of resistance R= 220 ohm, an inductor of inductance L=290 mH, and a voltage source with potential difference V=10.0 V(Figure) At some time t after the switch is closed, the current through point B is I_B=13.0 mA. At this time, what is the rate of change delta I_b/deltat of the current through point B? Find the value of I_b/t at time t. Express your answer in amperes per second to three significant figures.

Solution

Voltage across R_B is

V_B=I_BR_B =(13*10^-3)*220

V_B =2.86 Volts

Voltage across inductor

V_L=V-V_B =10-2.86

V_L=7.14 Volts

since V_L=L(dI_B/dt)

7.14 =(290*10^-3)*(dI_B/dt)

=>(dI_B/dt) =24.62 A/s