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Title of Experiment: Kirchhoff’s
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Rules
Gustav Robert Kirchhoff
(1824-1887) – German Physicist
Introduction and Objectives:
Kirchhoff’s rules can be used to analyze complex circuits containing several resistors and
voltage sources. There are two rules:
i) The sum of currents entering any junction must equal the sum of the currents leaving that
junction (this is also called the “junction rule”)
ii) The sum of the potential differences across all the elements around any closed circuit loop
must be zero (this is also called the “loop rule”)
Equipment Required:
Two 100 Ω and one 470 Ω resistor, current sensor or ammeter, voltage sensor or multi-meter, 3
1.5V batteries, battery connector, connecting wires.
Lab Procedures:
Set up a circuit as shown in the figure. Use batteries or a power supply for E1 and E2. Use
resistors R1 (470 Ω), R2 (100 Ω) and R3 (100 Ω).
Measure the actual voltages for each battery using a multi-meter or voltage sensor and record
these values in Table 1.
Using Kirchhoff’s rules, and the actual values of the voltages (E1 and E2) calculate the current in
loops 1 and 2.
Measure the actual values of the currents in each loop using an ammeter or current sensor. Enter
your results in Table 1 and calculate the respective percent errors.
R1 = 470Ω
Loop 1
E1 = 3V
Loop 2
R2= 100Ω
I1
R3= 100Ω
I2
E2 = 1.5V
1
Setting up the circuit:
Ammeter
E2 = 1.5V
Loop 2
Loop 1
E1 = 3V
2
Close-up of resistors in circuit:
R1
R3
R2
-ve 1.5V
-ve 3V
+ve 3V
+ve 1.5V
How to connect an ammeter:
Positive lead going to ammeter/Curent sensor
Negative lead from
ammeter/ Current
sensor
3
Table 1
Experimental values (measured by instruments):
Current in loop 1 (i1) Current in loop 2 (i2) Voltage for battery 1
(E1)
Voltage for battery 2
(E2)
Calculations:
Some guidelines to follow:
i) Define a current i1 for loop 1 and i2 for loop 2.
ii) The directions of the currents in these loops for calculation purposes is arbitrary. We can take
either a clockwise direction or counterclockwise direction. In our figure, we choose the
clockwise direction for the currents i1 and i2.
iii) By convention if you move from the negative pole of a battery to the positive pole, the sign
of the voltage is positive (because you are moving from a low voltage to a high voltage) and vice
versa.
iv) If you move in the same direction as the direction of the current, the sign of the voltage is
negative, example –iR.
R1 = 470Ω
Loop 1
E1 = 3V
Loop 2
R2= 100Ω
i1
R3= 100Ω
i2
E2 = 1.5V
4
Using the above conventions, and Kirchhoff’s loop rule (The sum of the potential differences
across all the elements around any closed circuit loop must be zero), we can set up equations for
the sum of voltages in each loop and equate them to zero:
Loop1:
+E1 - i1R1 –i1R2+i2R2 = 0
Substitute values for E1 and R into the above the equation:
Equation I:
Loop2:
+E2 – i2R2 +i1R2-i2R3 = 0
Substitute values for E2 and R into the above the equation:
Equation II:
Now use Cramer’s rule to solve for i1 and i2:
If:
a1x + b1y = c1
a2x + b2y = c2
then:
5
Results:
Using Kirchhoff’s Rules (Calculations):
Current in Loop 1
Current in Loop 2
Using Ammeter/Current sensor:
Current in Loop 1
Current in Loop 2
Use the formula for percent error to determine the percent error. (“A” = “Accepted” = values
determined with Kirchhoff’s rules, (“E” = “Experimental” = values determined with
Ammeter/Current sensor):
Percent errors:
Current in Loop1
Current in Loop2
Conclusions:
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