Calculating the average power supplied by a source

[TheBigDig]

1. For the circuit shown in (Figure 1) , where V= 2.8 cos(2 t+ 0.3 ) , R= 8 Ω and C= 4×10−2 F , find the average power supplied by the source, P_s and the average power absorbed by the resistor P_R .2. p (t) = v(t)i(t) = V_mI_m cos (ωt + θ_v) cos (ωt + θ_i)
P_R = (1/2)(V²_m/R)3. From the expression given, I've managed to isolate the value of omega and V_m. But I'm confused as to how to find the power if we're not given an expression for the current.

 

[vela]

You're supposed to derive one from your knowledge of $V_m$ and the circuit.

 

[cnh1995]

1. For the circuit shown in (Figure 1) , where V= 2.8 cos(2 t+ 0.3 ) , R= 8 Ω and C= 4×10−2 F , find the average power supplied by the source, P_s and the average power absorbed by the resistor P_R .2. p (t) = v(t)i(t) = V_mI_m cos (ωt + θ_v) cos (ωt + θ_i)
P_R = (1/2)(V²_m/R)3. From the expression given, I've managed to isolate the value of omega and V_m. But I'm confused as to how to find the power if we're not given an expression for the current.

I think you are complicating the problem. This is a series RC circuit excited with an ac source. You know the resistance and capacitance. What is the capacitive reactance? What is the total impedance of the circuit?

 

[TheBigDig]

I think you are complicating the problem. This is a series RC circuit excited with an ac source. You know the resistance and capacitance. What is the capacitive reactance? What is the total impedance of the circuit?

So I found the reactance to be equal to -12.5j S and the total impedance to be 8-12.5j Ω. Am I right in saying that I can then use the Y = 1/Z = I/V relation to find the current?

 

[cnh1995]

So I found the reactance to be equal to -12.5j S and the total impedance to be 8-12.5j Ω

Yes.

Am I right in saying that I can then use the Y = 1/Z = I/V relation to find the current?

Yes. You can also use the magnitude of impedance and voltage to calculate the magnitude of current, and then calculate the power consumed by the resistor.

 

[TheBigDig]

Yes.

Yes. You can also use the magnitude of impedance and voltage to calculate the magnitude of current, and then calculate the power consumed by the resistor.

Yes.

Yes. You can also use the magnitude of impedance and voltage to calculate the magnitude of current, and then calculate the power consumed by the resistor.

Thanks so much. Got the answer in the end. You were a terrific aid.