Alternating Current — Question 10

Question 10

A measured delay fixes relative phase only after the period is known

A voltage $v=V_p\cos\omega t$ has period 8.00 ms. A sinusoidal current of the same frequency reaches its positive maximum 1.00 ms after the voltage maximum. Assume the delay is within one cycle.

1. Find the current phase lag and write i(t).

2. Find current at a voltage maximum and at the next voltage zero crossing.

Question 10 - Solution

A measured delay fixes relative phase only after the period is known

(a) Method and calculation

$$\phi=\omega\Delta t=2\pi(1/8)=\pi/4.$$$$\boxed{i(t)=I_p\cos(250\pi t-\pi/4)}.$$

(b) Interpretation and further calculation

$$i(0)=I_p\cos(-\pi/4)=I_p/\sqrt2.$$$$\boxed{i(T/4)=I_p\cos(\pi/2-\pi/4)=I_p/\sqrt2}.$$

Physical check

Equal instantaneous current values can occur while its slope has opposite signs.