Question

if vdc=2v what will be the value of vm

Answer 1

we know,
$\bold{V_{dc}=\frac{1}{T}\int\imits^T_0 {V(t)}\,dt}$
Here, T is time period ,
V(t) = Vmsinωt

Now, $\bold{V_{dc}=\frac{1}{2\pi}\int\imits^{2\pi}_0 {V_msin\omega t}\,dt}\\\\\bold{=\frac{1}{2\pi}[\int\limits^{\pi}_0 {V_msin\omega t}\,dt+\int\limits^{2\pi}_{\pi} {0}\,dt}]\\\\\bold{=\frac{1}{2\pi}V_m[-cos\omega t]^{\pi}_0}\\\\\bold{=\frac{V_m}{\pi}}=\bold{0.318V_m}$

Hence, Vdc = 0.318Vm
If Vdc = 2V then, Vm = 2v/0.318 = 6.28v