Question

Problem 3: Branches and Loops II (25pts). Consider the following circuit: Ri=521 = 12 V D WB+C V = 6 v L R =1003 ER-52 V - 24V E Ri= 150 1. Identify the branches and the loops of the circuit. 2. Using Kirschoff's rules and the loop current method, calculate the voltage and the current across each resistor. 3. Calculate the electric power dissipated in each resistor.

Answer 1

The given circuit is, Resson 6V-T' fRegion L24V 11+: H FR615.. Branches :- the element between two nodes is called "Banch": No. of Branches in the given circuit = 7 Loops closed path formed by the branches in the circuit is called "Loop". No. of loops in the given circuit = 3

- Apply loop Analysts -6+51, +10 (I, - Iz) =o . 151,-10 In = 610 folk I, s. to (1x7,) +12 +5(1- 1.)-0. 15 12 -101, - 515=-12 ~ 75 (Is-Iz) -24 +15(Is) - 2015 -5 I ₂ = 24 → By solving we get 4, 12 &I I, = 0.2114 I 2 = -0.282A Is=1.1294

o Voltages and currents at each Resistors is atri 2) IR, = 1, = 0.211 Amp & Veg - IR, XR = 0.2 11X5=1.050 oth IR 2 = 1 I, I, = 0.493A & VR2 = I 22 XR, = 4.934 at 2 ay IR 3 =122 - Isl=1.41A & Ves = IR 3 XR₂ = 7,054 atte FR y = I3 = 1.129 A & VRG = IR 4X R4 = 16.9350 ③ Electric power at each Resistor is at Ri Peru Pēr XR, =(0.211) **5 = 0.2.26 watt stop Dj xki =(6.493}}x10=2.43 watt DES XR4=(1:41)**5=9.94 watt I at Ry Peugia Pžu x R4 =(1,129)}x15= 19.11 2 watt