Practice Problems: Kirchhoff's Rules Solutions

1. (moderate) A student claims that a loop rule applied to a simple electric circuit confirms the principle that charge is conserved. Is the student correct? Explain your response.
The student is not correct. The loop rule is based upon energy conservation. As charges move around the loop they experience various changes in electric potential. Since charge multiplied by electic potential is electric potential energy, the loop rule quantifies the fact that in a closed circuit loop there is no net gain of energy. Perhaps the student is confusing the loop rule with the point rule as point rule is associated with charge conservation.

2. (moderate) A simple electric circuit is analyzed by a student such that the following loop rule accurately describes the how electric potential changes in the loop.
12 - 15I - 25I - 9I = 0
Determine the current in the loop and then create a graphical representation of this loop rule. Assume that one point in the loop is grounded.



3. (moderate) Use Kirchhoff's rules to determine the meter readings in the circuit shown below.


By the loop rule:
50 - 5I - 10 I - 5I = 0
50 = 20I
I = 2.5 A
(This is the ammeter reading)
For resistors, V_R = IR
For each 5 Ω resistor: V₅ = 2.5(5) = 12.5 v
(This is the reading on the top and on the bottom voltmeters)
For the 10 Ω resistor: V₁₀ = 2.5(10) = 25 v
(This is the reading on the left voltmeter)
For remaining voltmeter: V = V₅ + V₁₀ = 12.5 + 25 = 37.5 v

4. (moderate) Find the potential difference V_AB in the circuit shown below.

5. (moderate) Find the currents in the circuit shown below.

6. (moderate) Find the voltage drop across each resisistor in the circuit shown below.

7. (moderate) Find the potential difference V_AB in the circuit shown below.