Sinusoidal steady state circuit

In summary, the circuit has a voltage source of 2sin(2t + 45) and is purely resistive, so the current phase will not be affected anywhere in the circuit. The currents can be solved for using a DC source of 2V, and then the sin(2t + 45) can be added back to the results. The final solution should be in the format of Isin(2t + 45) or I[sin(2t) + cos(2t)]. The magnitude of both currents is √2/2 and the currents in the loops are I1 = 2, I2 = 1, I3 = 1. The current from the supply is Ia =
  • #1
magnifik
360
0
I am trying to find the indicated currents for the following circuit, given v1 = 2sin(2t + 45):
m80hkz.jpg


I attempted to solve it in the following way:
v1 = 2sin(2t+45) // given
= 2[sin(2t)cos(45) + cos(2t)sin(45)]
= √2[sin(2t) + cos(2t)]

I use a matrix for the loops:
A =
[2 -1 -1
-1 3 -1
-1 -1 3]

b =
[√2
0
0]

I'm wondering what format the final solution should be in. Should it be Isin(2t+45) or I[sin(2t) + cos(2t)]?

Btw, I got √2/2 for the magnitude of both the currents.
Any input is appreciated. Thanks in advance.
 
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  • #2
Since the network is purely resistive it won't muck about with the current phase anywhere in the circuit. So I'd solve for the currents as though it were a DC source of 2V. Tack the sin(2t+45) back onto the results you get and call it a day!
 
  • #3
gneill said:
Since the network is purely resistive it won't muck about with the current phase anywhere in the circuit. So I'd solve for the currents as though it were a DC source of 2V. Tack the sin(2t+45) back onto the results you get and call it a day!

ok. thank you.
 
  • #4
I got 1 as the magnitude for both of the currents so i = sin(2t + 45)
 
  • #5
magnifik said:
I got 1 as the magnitude for both of the currents so i = sin(2t + 45)

I find that Ia is not the same as Ib. Perhaps you can check your matrix calculation?
 
  • #6
I got I1 = 2, I2 = 1, I3 = 1
where I1 is the current in the loop on the left part of the circuit, I2 is the current in the top part of the circuit, and I3 is the current in the loop of the right part of the circuit.

Ia = I1-I2 = 1
Ib = I3 = 1
 
  • #7
magnifik said:
I got I1 = 2, I2 = 1, I3 = 1
where I1 is the current in the loop on the left part of the circuit, I2 is the current in the top part of the circuit, and I3 is the current in the loop of the right part of the circuit.

Ia = I1-I2 = 1
Ib = I3 = 1

Yes, you're right! I was thinking that Ia was the current from the supply. I must be getting tired :rolleyes:
 

1. What is a sinusoidal steady state circuit?

A sinusoidal steady state circuit is an electrical circuit that is operating under the assumption of steady state conditions, meaning that the circuit has been running for a long time and all voltages and currents have reached a constant value. The term sinusoidal refers to the type of input signal, which is a sine wave.

2. What is the significance of sinusoidal steady state in circuit analysis?

Sinusoidal steady state is significant in circuit analysis because it allows us to simplify the analysis of complex circuits by assuming that all voltages and currents are constant and represented by phasors. This makes calculations easier and more efficient.

3. How is the frequency of a sinusoidal steady state circuit determined?

The frequency of a sinusoidal steady state circuit is determined by the frequency of the input signal, which is usually given in hertz (Hz). This frequency remains constant in a steady state circuit, regardless of the changes in voltage or current.

4. What are the key components of a sinusoidal steady state circuit?

The key components of a sinusoidal steady state circuit include resistors, capacitors, and inductors. These components are used to create a variety of circuit elements, such as filters, amplifiers, and oscillators, which are essential for many electronic devices.

5. How is the analysis of a sinusoidal steady state circuit different from a non-sinusoidal circuit?

The analysis of a sinusoidal steady state circuit is different from a non-sinusoidal circuit because it uses phasors to represent voltages and currents, rather than the traditional instantaneous values. In addition, the analysis of a sinusoidal steady state circuit is focused on the steady state behavior, while a non-sinusoidal circuit may involve transient behaviors and time-varying signals.

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