# Voltage source vs capacitor

1. Jun 7, 2013

### JustStudying

If we have a circuit (see attached)
will our voltage source's supplied voltage be delayed by the capacitor in anyway?
(as the voltage across a capacitor lags the current through a capacitor by 90 degrees)
then, as the resistor,voltage source, and capacitor are all in parallel does this
cause the voltage source to end up supplying a 'lagging' voltage (due to the capacitor's characteristics)?

OR is the capacitor forced to experience whatever the voltage source is supplying?
(therefore causing the inductor current to lead the capacitor by 90 deg)

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2. Jun 7, 2013

### BruceW

That's it. We assume that the voltage source is able to do what it is supposed to, regardless of what is going on in the circuit. And you are right, the current will lead the voltage by 90 degrees.

3. Jun 7, 2013

### Staff: Mentor

Inductor? Resistor? What is it?

Resistor current lags the capacitor current by 90°.

4. Jun 7, 2013

### rude man

Right.
What inductor current? What inductor?

EDIT:

If the voltage source is dc: for the capacitor, i = C dV(t)/dt. Since dV(t)/dt is infinitely large (going from 0 to V in zero time), the current is infinite for an infinitely short time.

Mathematically, V(t) = V U(t), the unit step function, and i(t) = CV δ(t) where δ(t) is the Dirac delta function with dimension T-1.

If the source is a sinusoid, which it just dawned on me it probably is, then yes, the current will lead the voltage by 90 deg. and its magnitude is wCV, w = 2 pi f.

Last edited: Jun 7, 2013
5. Jun 7, 2013

### BruceW

@NascentOxygen agreed. and when he says "inductor current", I was assuming he just meant current through the voltage source. Although "inductor current" is a term I have not heard before in this context...

6. Jun 7, 2013

### BruceW

@rude man - From the OP, I would guess that he/she is supposed to assume sinusoidal voltage

7. Jun 7, 2013

### rude man

Yesd, that just dawned on me. Thanks.

8. Jun 7, 2013

### JustStudying

sorry! i meant the capacitor current when i said 'inductor current' - got mixed up reading my notes over and over, thanks guys!

9. Jun 7, 2013

### JustStudying

So in this case, the current through the resistor should be in phase with the voltage supply, while the current through the capacitor leads the capacitor voltage by 90 deg am I correct?

Last edited: Jun 7, 2013
10. Jun 8, 2013

### Staff: Mentor

You now realise you are really stating nothing new. "The current through the resistor is always in phase with the voltage across that resistor", while "the current through the capacitor always leads the capacitor voltage by 90 deg".

11. Jun 8, 2013

### BruceW

yep. you got it.