Question

A series LR circuit contains an emf source of 19 V having no internal resistance, a resistor, a 22 H inductor having no appreciable resistance, and a switch. If the emf across the inductor is 80% of its maximum value 4 s after the switch is closed, what is the resistance of the resistor

Answer 1

Answer: R = 394.36ohm

Explanation: In a LR circuit, voltage for a resistor in function of time is given by:

`V(t) = \epsilon. e^{-t.(L)/(R) }`

ε is emf

L is indutance of inductor

R is resistance of resistor

After 4s, emf = 0.8*19, so:

`0.8*19 = 19. e^{-4.(22)/(R) }`

`0.8 = e^{-(88)/(R) }`

`ln(0.8) = ln(e^{-(88)/(R) })`

`ln(0.8) = -(88)/(R)`

`R = -(88)/(ln(0.8))`

R = 394.36

In this LR circuit, the resistance of the resistor is 394.36ohms.