Question

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R1 ii iz www EI E2 R₃ Question 3 (20 pts) In the figure on the right, the ideal batteries have emfs Ei= 10 V and E2 = Ez = 6 V and the resistors are identical with R = 5 ohm. (a)(10pts) Apply Kirchhoffs loop and junction rules and obtain three independent eqaations to solve three unknown currents ii, i2, and iz as shown in the figure and solve for the current i1. That is, what is the magnitude and direction of li? (b)(5pts) What is the magnitude and direction of i2? (c)(5pts) What is the total energy dissipation rate in all the resistors (d)(5pts) Prove that total power supplied to the circuit by the batteries are equal to the total power loss in all the resistors. i2 E 3

Answer 1

d ia Rg E2 I e Given, E, = lov , &2 = 43 = 6V , R=sor = R = R₂ = R3 (a) 5 using kri in closed doop (ab efa), - iqrq - & -itr, + &, = 0 -& & & & iz R2 + 2q R, = 0 +6 +5i, +5 in = 0 5 i +5 12 = 4 g + ²a = 4 + 2q + €, = 0.8A -) resing kve in clored top (bedeb), - Ez in iz Rz + 4 + ² R₂ = 0 3-6 - 583 + 6 + 52, = 0 {q - = 0 2 resing KCL in junction e, iq = iz + 3 - from @l, we get, èg = 2 ł, = 2 g - from equi & G iztiz t i = 0.8 3 i = 0.8 = 0.267A = in from, lt), ég = 2xig = 0.533 A: ->>

found that 0.533 A from the above results, we i, iq = 0.267A ig = 0.267A. The magnitude of f = 0.533A direction clockwise. Hence, E) os right The 0-264 A direction magnitude of ra downward. (10) The magnitude of iz = 0.267 A direction clockwise right (3) 08 es Resistor es given by for Energy dissipation rate in each POVIĆ IZR he = I, R = 10.533)2(5) = { I2R = (0.267) ² (s) = I ² R = (0.267)² (5) =0-355556 w (04222 w for Q2 - 03355 S56W for Ris, & Total Energy dissipation rate is given by, Ptotal + + = 1.4222 W +0.355556Wt 0*355556 W Protal. Protal 2.1333 w d) ६।९ Power supplied by the batteries, l' net » Pret = & itte, 22) +Eziz) -> Pret = (10x (0-5 33) ) PCX 6x0.267) +EX 6X0-267) 3.19999 =) Pret 5.333 - Poret = 2.1333 W from part © we got, sotal power loss in all the resistors es Ptotal = 2.1333w and an part (d) total power supplied by the batteries is Preta 2013 334 Hence, Power supplied by batteries is equal to powerloss by Resistans