In the circuit shown in the figure below we want to solve for the currents I_1,
ID: 1606732 • Letter: I
Question
In the circuit shown in the figure below we want to solve for the currents I_1, I_2 and I_3 as shown by arrows in the diagram. (a) How many junction points arc there in the circuit below? Name them (b) Using the junction rule (Current equation) write down the currents for each of these junctions. (c) Using the loop rule (Voltage equation) write down the equations for the loops (i) abfea (ii) abdea (iii) efdce (d) How many equations do we need if we tried to solve for the currents I_1, I_2, I_3? Write them (e) Solve for the currents I_1, I_2 and I_3 with their proper directionsExplanation / Answer
a)
There are two junctions 'a' and 'b'
b) at 'a'
I3 = I1 + I2 ( sum of incoming = sum of outgoing)
at 'b'
I1 + I2 = I3-------------------(1)
c)
1) abfea
(3*I2) - 10 + (3*I2) + (1 * I3) + (10*I3) = 0
(6 * I2) + (11 * I3) - 10 = 0 ---------------(2)
2) abdca
(3*I2) - 10 + (3*I2) - (5 * I1) - 4 - (5 * I1) = 0
(6 * I2) - (10 * I1) - 14 = 0 -----------------(3)
3) efdce
(-10 * I3) - (1 * I3) - (5 * I1) - 4 - (5 * I1) = 0
-(11 * I3) - (10 * I1) - 4 =0 -----------------------(4)
d)
we need 3 equations to solve
I1 + I2 = I3-------------------(1)
(6 * I2) + (11 * I3) - 10 = 0 ---------------(2)
(6 * I2) - (10 * I1) - 14 = 0 -----------------(3)
solving (1), (2) and (3)
I1 = 0.75 A (opposite to the direction shown in fig)
I2 = 1.07 A
I3 = 0.32 A
I2 and I3 are same direction as shown in fig