Question III.2: (a) Calculate the current I using the superposition theorem ...
(a) Calculate the current I using the superposition theorem for the circuit shown in Fig. 24.
(b) Find the equivalent resistances connected between three terminals A, B and C in star connection for a given delta connection witn three resistances R_{AB}, R_{BC} and R_{CA} between terminals A, B and C.
(a) We will consider the 75 V source first and short circuit the 64 V source. The current supplied by the 75 V source will be calculated. From the total current, current flowing through the resistor across terminals A and B will be calculated. The steps are illustrated in Fig. 28. When 64 V is short circuited, the 12 Ω and 4 Ω resistors get connected in parallel.
From Fig. 28(e), the battery current calculated is 7 A and the current through the 5 Ω resistor across terminals A and B is calculated using the current divider rule in Fig. 28(b) as
I_{1}=7 \times \frac{20}{20+5+3}=5 AThis 5 A through the resistor is due to the voltage source of 75 V. Now, we will calculate the current through the same resistor due to the other voltage source. We will short circuit the 75 V source and proceed as follows.
Current, I=\frac{64}{4+108/21}=\frac{64}{84+108/21}=\frac{64 \times 21}{192}=7 A
Current I_{1} through the parallel circuit BAC in Fig. 29(b), is calculated as
I_{1}=I \times \frac{12}{5+4}=7 \times \frac{12}{9+12}=4 AThrough the resistor across terminals AB, current of 5 A flows from A to B due to voltage source of 75 V and a current of 4 A flows from B to A due to voltage source of 64 V. The net current I_{AB} is equal to I_{AB} = 5 − 4 = 1 A when the effect of both the voltage sources are superimposed.
(b) Refer to Section 2.9.1 on Page 2.60.
