1. Use superposition to calculate the magnitudes of all currents in the circuit shown below (show all work):
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Can someone please help on this question.
i3 = i1 - i2
Vb = 680 i3
Vb = 5 + 1000 i2
10 = 330 i1 + Vb
To calculate the magnitudes of all the currents in the given circuit using superposition, we need to follow these steps:
Step 1: Remove all independent sources one by one, while keeping the dependent sources intact. We will analyze the circuit separately for each independent source.
Step 2: Replace each independent current source with an open circuit (or voltage source with 0V) and each independent voltage source with a short circuit (or current source with 0A).
Step 3: Calculate the currents in the circuit in response to each independent source separately and then combine them algebraically.
Step 4: Finally, compute the total current by summing up the currents calculated in each step.
Let's solve the circuit step by step:
Step 1: Remove the independent voltage source (V1 = 20V) and analyze the circuit with only the current source (I2 = 6A) active.
Step 2: Replace the voltage source V1 with a short circuit (0V), as we removed it in step 1.
Step 3: Now we can calculate the currents in the circuit produced by I2 = 6A.
To solve the circuit, we can use Kirchhoff's voltage law (KVL) around each loop:
For the outer loop:
-10I3 + 2(I1 - I2) + 4(I1 - I3) = 0
For the inner loop:
4(I3 - I1) + 6 + 2(I2 - I1) = 0
Solving these two equations simultaneously will give us the values of I1, I2, and I3.
Step 4: Once we have the values of I1, I2, and I3 for the current source I2 = 6A alone, we need to repeat the steps for the independent voltage source V1 = 20V alone.
Follow the same procedure as in Steps 1 to 3, but this time, remove the current source (I2 = 6A) and replace it with an open circuit (no current flows through it).
Again, solve the modified circuit equations to find the values of I1, I2, and I3.
Step 5: Now that we have the values of I1, I2, and I3 for each independent source alone, we can calculate the total currents.
Add the values of each current:
I1_total = (I1 from step 3) + (I1 from step 4)
I2_total = (I2 from step 3) + (I2 from step 4)
I3_total = (I3 from step 3) + (I3 from step 4)
These values will give you the magnitudes of all currents in the circuit.