Homework SourseUse Kirchoffs laws to calculate the theoretical value for th
Use Kirchoff\'s laws to calculate the theoretical value for the current in each branch of Circuit I shown in the diagram below. Use values of the resistors and emf\'s that are given. Analyze the circuit by writing the appropriate equations using Kirchoff\'ss laws. Use our calculator to solve simultaneous equations. Find currents I1, I2, and I3, with switches S1 CLOSED and S2 OPEN.
R1 ~ 100 R3-1000 R3~270 13 R2 S2 12 Circuit 1-To be investigated in lab Solution
first we consider S1 and S2 closed and apply Kirchoff’s rules to each loop
left loop algebraic sum of the emfs in a closed loop is 0
S1:
E1-I2R2-I1R1 =0
5-1000I2-100I1 =0
100I1+1000I2 =0 -------(1)
S2:
E2+I3R3-I2R2 =0
12 +270I3-1000I2 =0
270I3 – 1000I2 =-12 --------(2)
apply junction rule at the top
I1= I2 +I3
replace I3 from (2)
270(I1-I2) -1000I2 = -12
270I1 -1270I2 = -12 ---(3)
I1 = -0.014 A
I2 = 0.0064 A
I3 = I1-I2 = -0.014-0.0064 = -0.0204 A
with S1 closed and S2 open
I2 =0
I1 = I3
apply loop law for the single loop
E1=I1R3+I1R1
5 = 270I1+100I1
I1 = 5/370 = 0.135 A
