In the Circuit shown above find Thevenin Voltage for V0 in f

In the Circuit shown above, find Thevenin Voltage for V0 in function of the impedances ZR, ZL, ZC and the Phasor Voltage in Vi.

a) V0 = Vi*(ZR)/(ZR+ZL+ZC)

b) V0 = Vi*(ZC)/(ZR+ZL+ZC)

c) V0 = Vi*(Zl + ZC)/(ZR+ZL+ZC)

d) V0 = Vi*(Zl + ZC)/(ZL + ZC)

Generic electrical schematic of a simple band-stop filter

Solution

Here R, L and C form a loop with the voltage source Vi. So, the series current Ii

due the voltage source Vi is, if the current is Ii,

Ii=Vi/(ZR+ZL+ZC) Ampere

Now the Thevenin voltage across the open ended terminal is basically the voltage drom across the branch comprises of L and C.

so, the drop across series L-C path is the basically the Vo.

So, Vo=Ii * (ZL+ZC)

again the above expression can be written as putting the value of Ii,

Vo=(Vi/(ZR+ZL+ZC)) *(ZL+ZC)

Vo=Vi*(ZL+ZC)/(ZR+ZL+ZC)

So, option (c) is the correct answer.