Find the power P consumed by the resistor R4 shown in Figure-P4 Vs1 = 12 Volts,

Question

Find the power P consumed by the resistor R4 shown in Figure-P4 Vs1 = 12 Volts, Vs2 = 5 Volts , R1 = 50 Ohm, R2 = 20 Ohm R3 = 20 Ohm, R4 = 20 Ohm, and R5 = 15 Ohm

Explanation / Answer

let the current through left side loop is i1 in clockwise direction,current through right side top loop is i2,and for bottom as i3 are in clock-wise direction Applying KVL for the loops, Vs1-i1R1-(i1-i2)R2-(i1-i3)R3=0--->A Vs2-(i1-i2)R2+(i2-i3)R4=0---->B (i1-i3)R3+(i2-i3)R4-i3R5=0---->C A--->12-i1(50)-(i1-i2)20-(i1-i3)20=0 12-90i1+20i2+20i3=0 90i1-20i2-20i3=12 4.5i1-i2-i3=0.6-------->A1 B--->5-(i1-i2)20+(i2-i3)10=0 5-20i1+30i2-10i3=0 i3=3i2-2i1+0.5------>B1 C---->(i1-i3)20+(i2-i3)10-15i3=0 20i1+10i2-45i3=0 i2=4.5i3-2i1---->C1 Keep C1 in A1 4.5i1-4.5i3+2i1-i3=0.6 6.5i1-5.5i3=0.6 i1-0.846i3=0.0923----->A2 Keep C1 in B1 i3=3*(4.5i3-2i1)-2i1+0.5 8i1-12.5i3=0.5 i1-1.5625i3=0.0625---->B2 subtracting B2 from A2 (1.5625-0.846)i3=0.0923-0.0625 i3=0.0416A i1=0.1275A i2=-0.0678A [negative sign indicateds the direction of current is opposite to assumed direction] power consumed by R4=i^2R4 =(i2-i3)^2 *10 =(0.0678+0.0416)^2 *10 =0.11967W

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