Source Transformation to Solve a Circuit Find the

Source Transformation to Solve a Circuit Find the power associated with the 6 V source. State whether the 6 V source is absorbing or delivering power to the circuit. ECE 201 Circuit Theory 1 1

Which method to solve? Use mesh-current method and solve for the current in the 6 V source. (3 equations) Use node-voltage method and solve for the voltage across the 30Ω resistor and calculate the current delivered by the 6 V source. ECE 201 Circuit Theory 1 2

Use Source Transformation to “focus in” on the branch containing the 6 V source. CAUTION --- Preserve the identity of the branch containing the 6 V source! ECE 201 Circuit Theory 1 3

Step 1 -- Transform the 40 V source ECE 201 Circuit Theory 1 4

Step 2 (a) -- combine the 20Ω and 5Ω resistors into an equivalent 4Ω resistor. Req = 4Ω Step 2 (b) -- transform the equivalent 4Ω resistor and the 8 A current source into a 32 V source in series with a 4Ω resistor. ECE 201 Circuit Theory 1 5

Step 3 -- Transform the 32 V source in series with 20Ω into a 1. 6 A source in parallel with a 20 Ω resistor. ECE 201 Circuit Theory 1 6

Req = 12Ω Step 4 (a) -- Combine the 30Ω and 20Ω resistors into an equivalent 12 Ω resistor. Step 4(b) -- Transform the equivalent 12 Ω resistor in parallel with the 1. 6 A source into a 19. 2 V source in series with a 12 Ω resistor. ECE 201 Circuit Theory 1 7

i The final circuit has preserved the branch containing the 6 V source. The current can be determined by ECE 201 Circuit Theory 1 8

i The actual current is flowing from right to left, into the + terminal of the 6 V source. Therefore, the 6 V source is absorbing power. ECE 201 Circuit Theory 1 9