The current in an alternating-current circuit is given by i = 8.50sin(120t ). Find a function for

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The current in an alternating-current circuit is given by i = 8.50sin(120πt ). Find a function for the voltage v if the amplitude is 28V and voltage leads current by 45°. Then find the displacement. See Example 5.

Data from Example 5

In alternating-current (ac) circuits, voltage (v) and current (i) can both be represented by sine waves with the same period. Depending on the existence of resistors, capacitors, or inductors in the circuit, these waves can be in phase (maximums and minimums occur at the same time) or one can lead or lag the other. See Fig. 10.19.


If we assume that the sine wave for current passes through the origin, it can be represented as i = Im sin (2πft),  where f is the frequency (in cycles/s) and t is time (in s). The voltage can then be represented by v = Vm sin(2πft + ∅), m where ∅ is the phase angle.

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Basic Technical Mathematics

ISBN: 9780137529896

12th Edition

Authors: Allyn J. Washington, Richard Evans

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