Question

Write an expression for the instantaneous voltage V ( t ) delivered by an ac generator supplying 130 V rms at 65 Hz . Assume the voltage is 0 at time t = 0 , and leave the factors in exact form; do not round their values. Write the argument of the sinusoidal function to have units of radians, but omit the units.

Answer 1

Answer:

$V(t)=130\sqrt{2}\sin(130\pi t)V$

Explanation:

$V_r$ = RMS voltage = 130 V

f = Frequency = 65 Hz

Instantaneous voltage is given by

$V=\sqrt{2}V_r\sin(2\pi ft+\phi)$

$\\\Rightarrow V(t)=130\sqrt{2}\sin(2\pi 65t+\phi)\\\Rightarrow V(t)=130\sqrt{2}\sin(130\pi t+\phi)$

at t = 0 v = 0

$V(0)=130\sqrt{2}\sin(130\pi \times 0+\phi)\\\Rightarrow 0=130\sqrt{2}\sin(130\pi \times 0+\phi)\\\Rightarrow sin\phi=0\\\Rightarrow \phi=0$

So, the function is

$V(t)=130\sqrt{2}\sin(130\pi t)V$