Answer to Question #100918 in Electricity and Magnetism for fox

Question

a 2.0H solenoid is connected in serries with a resistor of total reisitance 5.0 ohms to 2.0V dc supply calculate 1. the final current 2.the initial rate of change of current with time 3. the rate of change of current with time when current is 2A

Answer 1

1.) In case of DC circuit, inductor acts a straight wire after a long time and acts as a wire of infinite resistance at t=0

so, we have to find the final current so at that time inductor will act as a wire of negligible resistance

Hence, final current= V/R=2/5 Amperes =0.4 A

2.) Expression for the Current in an LR Series Circuit, $I(t)$ $= \dfrac{V}{R}(1-e^{-Rt/L})$

rate of change of current with time=$\dfrac{V}{L}(e^{-Rt/L})$

at t=0, Rate of change of current = 1 A/s

3.) From Kirchhoff's voltage law

$V_s=IR+L \dfrac{dI}{dt}$

$2=2*5+2*\dfrac{dI}{dt}$

$\dfrac{dI}{dt}=-4$

here negative sign shows that there is decrease in current