The current in an alternating-current circuit is given by i = 12sin(120t). Find a function for the voltage v if the amplitude is 18V and

The current in an alternating-current circuit is given by i = 12sin(120πt). Find a function for the voltage v if the amplitude is 18V and voltage lags current by 60°. 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 = I_m sin (2πft),  where f is the frequency (in cycles/s) and t is time (in s). The voltage can then be represented by v = V_m sin(2πft + ∅), m where ∅ is the phase angle.

V In phase Voltage lags current Voltage leads current Fig. 10.19