But is it the same for AC circuits?

[harambe]

Homework Statement

For a series LCR circuit,the voltage across the resistance,capacitance and inductance is 10V each.If the capacitance is short circuited,the voltage across the inductance will be

(a)10V
(b)10/√2V
(c) 10/3v
(d)20V

Homework Equations

Potential difference across Inductance=I/XL
I=V/(R^2+(XL)^2)

The Attempt at a Solution

Okay so initially the capacitance,reactance as well as the inductance were equal
VR=VL=VC=10[/B]

Now VC=0 so It will act as a LR circuit whose voltage is given by

V=(VR)^2+(VL)^2

So how should I Calculate the new VR and VL?I think they will change from the first case because our circuit has changed but I am not too sure.If I apply the analogy of DC circuits then only current will change and reactance and inductance will remain same so I can calculate the Current.

 

[BvU]

So how should I calculate the V,VR and VL here?

Good question. But it doesn't count as an attempt at solution, so we can't help.

The general idea at PF is: you apply the relevant equations (where are yours?) to the known variables in order to derive the unknowns.

By way of (not really deserved ) hint: what else do you know of the voltage over C, L and R ?

 

[harambe]

(VR)^2+({VL)^2+(VC)^2}=(V)^2

From here the Voltage comes out to be 10V(Forgot to use this srsly)

 

[BvU]

How many equations with how many unknowns do you have now ?
My guess is you'll need something more... when is it that C and L have the same V ?

 

[BvU]

V=(VR)^2+(VL)^2

Something not quite right there ...

 

[harambe]

C and L have the same V at resonance

V={(VR)^+{(VL)^2-(VC)^2}} (Misplayed the negative sign)

 

[harambe]

*I found the Vrms to be 10V (Can this be maximum voltage instead of Vrms) *

Now I proceeded like this

R=XL

therefore since current will be same since they are in series

(I rms)= (V)^2/{(R)^2+(XL)^2)

(I rms)= 5√2/XL (R=XL)

So I calculated the VL=I rms x XL =5√2
I calculated after your hint but I am confused about the star statement

 

[BvU]

at resonance

Right. So the circuit is at resonance and you know XL = R. Bingo: post #7 is OK .

Whether V is rms or amplitude does not matter for the answer -- as long as problem statement and answer refer to the same.

(But it would have been nicer if the exercise had indicated one of the two)

 

[harambe]

Yea. Thanks for the help

 

[BvU]

You're welcome.