Solve RLC Circuit Problem - Get Help Now

[tiger95]

Hello, I have to solve the following problem but I don't know how to find the I(t) from I(ω). I've already found that the total impedance of the circuit should be (1000/29)-j(255/29). Can anyone help me, please? I haven't done Integration and Derivatives. Thank you for your help.

 

[gneill]

Hello tiger95, Welcome to Physics Forums.

Please note for future posts in the homework sections that it is mandatory to use the formatting template provided when the thread is started.

Since you have managed to calculate the impedance of the circuit (correct value but you forgot the units) then you should be able to use Ohm's law to find the total current. In phasor form the source voltage can be written as Vin = 2 V. That's a 2 V peak magnitude with no phase angle since the voltage source provides the reference angle. Peak values can be used here since you're not dealing with power calculations. If you were, you'd convert to RMS values.

Does that help you for part (a)?

 

[tiger95]

If I use Ohm's Law to calculate I(t) the result would be: I(t) = V / Z = 2 / (1000/29)-j(255/29) = (80/1469) + j(102/7345) but there isn't the time in the answer. Moreover, I haven't understood why the current will have the same phase as the voltage.

 

[gneill]

If I use Ohm's Law to calculate I(t) the result would be: I(t) = V / Z = 2 / (1000/29)-j(255/29) = (80/1469) + j(102/7345) but there isn't the time in the answer. Moreover, I haven't understood why the current will have the same phase as the voltage.

It won't have the same phase as the voltage. The voltage acts as a reference for the phase. The current will have a phase with respect to the voltage. What's the polar form of the current that you calculated?

The current that you found is the phasor form of the current. Convert to time domain by writing it as a cosine function, just as the voltage was written. The angular frequency is the same as the source and you should have the phase from the polar form of the current phasor.

 

[tiger95]

Here is how I managed to calculate I(ω) which I'm not sure it's right. Then, how can I change from I(ω) to I(t)?

 

[NascentOxygen]

Here is how I managed to calculate I(ω) which I'm not sure it's right. Then, how can I change from I(ω) to I(t)?

You already have I(t). You've called it I(ω) but you should have been calling it I(t) or maybe I(ωt) from the very start.

 

[tiger95]

Thanks to your hints, I managed to attempt a solution for the whole exercise. Can you confirm me that it's right, please?