The circuit shown in Figure (a) has been divided into two parts. In Figure (b),
ID: 2247987 • Letter: T
Question
The circuit shown in Figure (a) has been divided into two parts. In Figure (b), the right-hand part has been replaced with an equivalent circuit. The left-hand part of the circuit has not been changed. 812 16 72 V 32 48 24 8 72 V 32 (a) Determine the value of the resistance R in Figure (b) that makes the circuit in Figure (b) equivalent to the circuit in Figure (a) 32 (b) Find the current i and the voltage v shown in Figure (b). Because of the equivalence, the current i and the voltage v shown in Figure (a) are equal to the current i and the voltage v shown in Figure (b). V a (c) Find the current /2 shown in Figure (a) using current division 5 8 2 A 7 Determine the values of va and Vb, the node voltages at node a and node b: V and vb =Explanation / Answer
Answer:-a) From figure a, 24 and 48 are parallel hence equivalent is (24 x 48)/(24+48) Ohm = 16 ohm. This 16 ohm is in series with third resistor of value 16 Ohm as shown in figure a, so these series resistor give equivalent value of 32 Ohm which is the value of R in figure b. Hence R = 32 Ohm.
Answer:-b) In figure b, R and 32 Ohm are in parallel i.e the equivalent of these two is (32 x 32) / (32 + 32) = 16 Ohm. Next, this 16 Ohm and 8 Ohm are in series so equivalent value is 24 Ohm. Supply is of 72 V hence current out from supply is = 72/24 A = 3 A.
Now this 3 A currents gets divided between R and 32 Ohm(parallel resistors). Since both are of 32 Ohm, hence current will divide equally i.e 1.5 A through R and 1.5 A through 32 Ohm resistor. So i = 1.5 A.
Since R = 32 Ohm and Current through this is 1.5 A, hence voltage accross this, v = (i x 32) V = (1.5 x32) V = 48 V.
Answer:-c) We can see current i = 1.5 A gets divided among 16 Ohm and 24 Ohm. Since i2 is flowing through 16 Ohm resistor then (1.5 - i2 ) will flow through 24 Ohm resistor. Since both are parallel, both will have same voltage and hence using Ohm's law we can write-
i2 x 16 = (1.5 - i2) x 32 => 48 x i2 = 1.5 x 32, gives i2 = 1 A.
Answer:- Using KCL we can write-
2 - (Vb / 7) - (Vb - Va) / 5 = 0 => 12Vb - 7Va = 70--------------------------------(1)
(Vb - Va) / 5 = 2 + Va /8 => 8Vb - 13Va = 80--------------------------------(2)
On solving we get the result as - Va = - 4 V and Vb = 3.5 V
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