Use Kirchhoff\'s rules to analyze the circuit in the figure below. (a) Let I 1 b

Question

Use Kirchhoff's rules to analyze the circuit in the figure below.

(a) Let I1 be the branch current though R1, I2 be the branch current through R2, and I3 be the branch current through R3. Write Kirchhoff's loop rule relation for a loop that travels through battery 1, resistor 1, and resistor 3. (Use a clockwise current loop when entering your answer. Use any variable or symbol stated above as necessary.)


(b) Write Kirchhoff's loop rule relation for a loop that travels through battery 2, resistor 2, and resistor 3. (Use a clockwise current loop when entering your answer. Use any variable or symbol stated above as necessary.)


(c) Apply Kirchhoff's junction rule to the junction at A to get a relation between the three branch currents. (Use any variable or symbol stated above as necessary.)
I1 =  

(d) You should now have three equations and three unknowns (I1, I2, and I3). Solve for the three branch currents.

Explanation / Answer

let,

v1=1.5v and v2=3v

R1=2500 ohms, R2=1600 ohms, R3=4400 ohms

a)

by applying Kirchhoff's voltage rule for right side,

v2+i2*R2-i3*R3=0

3+i2*1600-i3*4400=0 ---(1)

by applying Kirchhoff's voltage rule for left side,

v1-i1*R1-i3*R3=0

1.5-i1*2500-i3*4400=0 ----(2)

by applying Kirchhoff's current rule at junction A

i1=i2+i3 ------(3)

from the equation (1), (2) and (3),

===>

i1=0.19 mA

i2=0.64 mA

i3=0.45 mA

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