PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity
Problem
In the circuit described below, a controlled (dependent) voltage source is used to model a sensing element that produces an emf proportional to a current elsewhere in the circuit.
• Loop 1 (left side) contains an ideal 10V battery in series with resistor R1=2.0Ω.
• Loop 2 (right side) contains resistor R2=6.0Ω in series with a controlled voltage source whose emf ϵc equals 5.0Ω⋅I3 (i.e., 5.0 Ω multiplied by the current I3 through a third resistor).
• The bottom branch common to both loops contains resistor R3=4.0Ω through which current I3 flows from left to right.
Assume conventional clockwise currents I1 in Loop 1 and I2 in Loop 2, with I3 defined as the current through R3 from left to right.
(a) Write two independent loop equations based on the information provided.
(b) Solve for the numerical values of I1, I2, and I3.
(c) Determine the numerical value of the controlled source’s emf ϵc.
(d) For the controlled source, state whether it is delivering power to the circuit or absorbing power from it, and justify your answer with a calculation.