Question

For the following pairs of sinusoidal time functions, determine which one leads/lags and by how much. (a) ????1(????)=4sin(6π×104????+60°) V and ????2(????)=2cos(6π×104????−20°) V. (b) ????(????)=10cos(400????−75°) V and ????(????)=4sin(400????+30°) A.

Answer 1

Answer:

The question is incomplete, the complete question is given below

"For the following pairs of sinusoidal time functions, determine which one leads/lags and by how much. (a) V1(t) =4sin(6π×10^4t+60°)V and V(t)2=2cos(6π×10^4t−20°)V. (b) V(t)=10cos(400t−75°) V and I(t)=4sin(400t+30°) A.

Answer

A. V2(t) leads V1(t) by 10°

B. I(t) leads V(t) by 15°

Explanation:

First we express the relationship between sine and cosine of a value.

The expression is giving below Cos (wt) =Sin(wt+90)

Hence for the equations above, we write

a. We can v(t) as

V1(t)=4Sin(6π*10^4+90°-30°)

V1(t)=4Cos(6π*10^4-30°)

Comparing to

V2(t)=4Cos(6π*10^4-20°)

Comparing the angle, we notice that V2(t) leads V1(t) by 10°

b. We can write the current wave form as

I(t)=4sin(400t+90°-60°)

I(t)=4Cos(400t-60°)

If we compare with V(t)=10cos(400t−75°)

I.e 4Cos(400t-60°)=10cos(400t−75°)

We can conclude that I(t) leads V(t) by 15°