A circuit consists of a coil that has a resistance equal to 6.06 and a self-indu

Question

A circuit consists of a coil that has a resistance equal to 6.06 and a self-inductance equal to 4.82 mH, an open switch, and an ideal 100-V battery—all connected in series. At t = 0 the switch is closed. Find the current and its rate of change at the following times. Time (ms) I (A) dI/dt (kA/s) (a) 0 (b) 0.100 (c) 0.500 (d) 1.00 A circuit consists of a coil that has a resistance equal to 6.06 and a self-inductance equal to 4.82 mH, an open switch, and an ideal 100-V battery—all connected in series. At t = 0 the switch is closed. Find the current and its rate of change at the following times.

Explanation / Answer

Current throught circuit

l = E(1 - e-tR/L) / R

energy stored in coil is

E = L*l^2 / 2

Rate of energy dissipated = Power P = l^2*R .....(1)

dE / dt = L*l*dl / dt ....(2)

From equation 1 and 2

L*l*dl / dt = l^2*R

L*d [ E(1 - e-tR/L) / R] / dt = l*R

L*(E / R) * (e-tR/L) * (R / L) =  E(1 - e-tR/L)*R / R

(e-tR/L) = 1 - (e-tR/L)

2*(e-tR/L) = 1

tR / L = ln(2)

t = L*ln(2) / R

t = 4.82*10^(-3)*ln(2) / 6.06

t = 0.551 ms

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