An ac generator has emf epsilon = epsilon_m sin(omega_d t - pi/4), where epsilon

Question

An ac generator has emf epsilon = epsilon_m sin(omega_d t - pi/4), where epsilon_m = 31.5 V and omega_d = 318 rad/s. The current produced in a connected circuit is i(t) = I sin(omega_d t - 3pi/4), where I = 732 mA. At what time after t = 0 does (a) the generator emf first reach a maximum and (b) the current first reach a maximum? (c) The circuit contains a single element other than the generator. Is it a capacitor, an inductor, or a resistor? (d) What is the value of the capacitance, inductance, or resistance, as the case may be? Number Units Number Units Number Units

Explanation / Answer

a) emf is maximum when sin(wdt - pi/4) = 1

318t - pi/4 = pi/2

t = 0.75 pi/318 = 0.00741 s

b)current is

maximum when sin(wdt - 3pi/4) = 1

318t - 3pi/4 = pi/2

t = 1.75 pi/318 = 0.0173 s

c) it is inductor since current is lagging

d) XL =31.5/0.732 =43.033

L = 43.033/wd = 43.0327/318 = 0.135 H

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