Final answer:
The first time after t=0 that the sinusoidal voltage equals 170V is approximately 0.159 seconds.
Step-by-step explanation:
The equation given is v = 170cos(120πt-60⁰), where v is the sinusoidal voltage. We are asked to find the first time after t=0 that v equals 170V. To do this, we need to find the value of t that makes the cosine term equal to 1. When the cosine term is 1, the voltage v will be at its peak value of 170V. Let's solve for that:
170 = 170cos(120πt-60⁰)
Dividing both sides by 170:
1 = cos(120πt-60⁰)
Since cos(θ) = 1 when θ = 0, we can set the argument of the cosine function equal to 0 and solve for t:
120πt-60⁰ = 0
120πt = 60⁰
t = 60⁰ / (120π)
t ≈ 0.159 seconds
Therefore, the first time after t=0 that v equals 170V is approximately 0.159 seconds.