RLC circuit and rate of increase of current

[hell-hawk]

Ok, I am having a problem with a RLC circuit and my teacher was unable to offer a satisfactory explanation. Hope that you'll help.
Consider a DC battery, a switch, a resistor, a capacitor and an inductor in series. Before t=0 the switch is open and assume that the circuit has achieved steady state. This means that the capacitor voltage is 0 and so is the inductor current. At t=0 the switch is closed. It follows that at t=0+ (i.e. just after t=0) the capacitor voltage will be 0 and so will the inductor current. It also follows that the voltage across the inductor at t=0+ will be V, i.e. the voltage of the source (the capacitor is acting as short-circuit and the inductor as open circuit). Therefore the rate of change of current in the circuit at t=0+ will be some positive value (from v=L di/dt). But the rate at which the capacitor voltage is increasing is ZERO at t=0+ (from i=C dv/dt; i=0). How could the rate of increase of current in the inductor be non-zero, but the rate of increase of voltage in the capacitor be zero? If one is increasing, shouldn't the other as well?
Please explain in physical terms and not mathematical. I'll be highly grateful.

 

[cyeokpeng]

I will try to explain as best that I can

Ok, I am having a problem with a RLC circuit and my teacher was unable to offer a satisfactory explanation. Hope that you'll help.
Consider a DC battery, a switch, a resistor, a capacitor and an inductor in series. Before t=0 the switch is open and assume that the circuit has achieved steady state. This means that the capacitor voltage is 0 and so is the inductor current. At t=0 the switch is closed. It follows that at t=0+ (i.e. just after t=0) the capacitor voltage will be 0 and so will the inductor current. It also follows that the voltage across the inductor at t=0+ will be V, i.e. the voltage of the source (the capacitor is acting as short-circuit and the inductor as open circuit). Therefore the rate of change of current in the circuit at t=0+ will be some positive value (from v=L di/dt)..

Up till here, you are correct!

But the rate at which the capacitor voltage is increasing is ZERO at t=0+ (from i=C dv/dt; i=0). How could the rate of increase of current in the inductor be non-zero, but the rate of increase of voltage in the capacitor be zero? If one is increasing, shouldn't the other as well?
Please explain in physical terms and not mathematical. I'll be highly grateful.

There is a slight misconception here. You are saying that the current i at time t=0 is zero, using the current continuity of the inductor i(0+)=0, i.e. physically, the current cannot have a discontinuity jump at time t=0. But there is no current continuity at the capacitor, i.e. at time t=0, i(0-)=0 AND
i(0+)=some value. So the rate of increase of capacitor voltage is NOT zero.
Hence the capacitor voltage is increasing at a positive rate together with the inductor current at time t=0+

I may be wrong, because it has been one year ago since I touch on this concept. If I am wrong, can someone please advice. Thanks.

 

[ravenprp]

In a RLC circuit, the inductor and capacitor store energy in the form of magnetic and electric fields, respectively. When the switch is closed at t=0, the circuit is no longer in steady state and the energy stored in the inductor and capacitor must be redistributed. This redistribution of energy causes the current in the circuit to change.

At t=0, the capacitor voltage is 0 and the inductor current is also 0. This means that there is no changing electric field in the capacitor and no changing magnetic field in the inductor. However, the voltage across the inductor is equal to the source voltage, which means that there is a changing magnetic field in the inductor. This changing magnetic field induces an electric field in the circuit, causing the current to increase.

On the other hand, the capacitor voltage does not change at t=0 because the current through it is 0. In order for the capacitor voltage to change, there must be a changing electric field in the capacitor. However, since the capacitor is acting as a short circuit, there is no changing electric field in the capacitor and therefore no change in voltage.

In summary, the rate of increase of current in the inductor is non-zero because there is a changing magnetic field in the inductor, while the rate of increase of voltage in the capacitor is zero because there is no changing electric field in the capacitor. This is due to the different ways in which the inductor and capacitor store and release energy in a circuit.