Superposition Theorem

Question: Using Superposition Theorem, find the current (I) through the 4ohms reactance inductor L2 in Fig 1. Show the answer both in Polar form and Rectangular form. Fig 1 L1 (XL) = 4 à ¢Ã¢â‚¬Å¾Ã‚ ¦, L2 (XL) = 4 à ¢Ã¢â‚¬Å¾Ã‚ ¦, and C1 (XC) = 3 à ¢Ã¢â‚¬Å¾Ã‚ ¦ V1 = 100 volts and V2 = 50 volts Answer: Using Superposition Theorem, find the current (I) through the 4ohms reactance inductor L2 in Fig 1. Show the answer both in Polar form and Rectangular form. Fig 1 L1 (XL) = 4 à ¢Ã¢â‚¬Å¾Ã‚ ¦, L2 (XL) = 4 à ¢Ã¢â‚¬Å¾Ã‚ ¦, and C1 (XC) = 3 à ¢Ã¢â‚¬Å¾Ã‚ ¦ V1 = 100 volts and V2 = 50 volts For considering Superposition theorem: First we have to take one source by short circuiting or open circuiting the other one 1 . First we take voltage source V1=10v (V2 =0,short circuited ) The value of Zeq by looking in to the network through V1 Zeq= XL1+ (XL2Xc1) XL2+Xc1 = 4+ 490 x3-90 /490+3-90 =4+ 12/j = 4 - j12 = 12.64-71.56 Total current I = 100/12.64-71.56 =0.7971.56 Applying current division rule IL2 =0.7971.56 x 3-90/490+ 3-90 = 2.3771.56 A = 0.75+ j2.25 2 . Considering the voltage source V2= 50 (V1 =0 ,short circuited) Applying KVL (as voltage across L1 is zero) 50 IL2Xc1- IL2XL2 =0 IL2 = 50/j =-5j A Total current flowing through Il2= Il2 +IL2 =0.75+j2.25-5j=0.75- j2.75A=2.85-74.7