Find the rms and peak currents in a 40-W, 120 v lightbulb. What is its resistanc

Question

Find the rms and peak currents in a 40-W, 120 v lightbulb. What is its resistance? A 50-kW electric heater is designed to run using 240-V ac source. Find its (a) peak current and (b) peak voltage. (c) How much energy will you be billed for in a 30-day month if it operates 2.0 h per day? The current in a resistor is given by I = (8.0 A) sin(40 pi t) when a voltage given by V = (60 V) sin(40 pi t) is applied to it. (a) What is the resistance value? (b) What are the frequency and period of the voltage source? (c) What is the average power delivered to the resistor? The current and voltage outputs of an operating ac generator have peak values of 2.5 A and 16 V, respectively (a) What is the average power output of the generator? (b) What is the effective resistance of the circuit it is in? The current in a 60-ohm resistor is given by

Explanation / Answer

V = 60 sin (40 pi t), the peak voltage V0 = 60 V

I = 8 sin (40 pi t), the peak current I0 = 8 A

a) R = V0/I0 = 60/8 = 7.5 ohm

b) The coffeicient of t is the angular frequency w = 40 pi

frequency f = w/2 pi = 40 pi / 2 pi = 20 Hz

Time period = 1/f = 1/20 = 0.05s

c) rms voltage Vrms = V0/ 21/2

rms current Irms = I0/ 21/2

Average Power in resistor is given by

P = Vrms * Irms = V0/ 21/2 * I0/ 21/2 = 60*8/2 = 240 W

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