Kirchhoff's Loop Rule
Help Questions
AP Physics C: Electricity and Magnetism › Kirchhoff's Loop Rule
A battery with emf $\varepsilon=18,\text{V}$ and internal resistance $r=2.0,\Omega$ is connected to an external load resistor $R=7.0,\Omega$ in series (single loop). Using Kirchhoff's Loop Rule, what is the potential difference across the battery terminals while delivering current to the load?
14.0 V
18.0 V
1.4 V
4.0 V
Explanation
This question tests AP Physics C concepts of applying Kirchhoff's Loop Rule with internal resistance. Kirchhoff's Loop Rule states that the sum of all voltage changes around a closed loop must equal zero. In this circuit, an 18V battery with 2Ω internal resistance connects to a 7Ω load. Applying the loop rule: 18V - I(2Ω) - I(7Ω) = 0, giving I = 18V/9Ω = 2A. The terminal voltage equals the emf minus the internal voltage drop: V_terminal = 18V - (2A)(2Ω) = 14V, making choice A correct. Choice B (18.0 V) is incorrect as it ignores the internal resistance effect. To help students: Emphasize that real batteries have internal resistance affecting terminal voltage. Practice problems involving power delivery and efficiency with internal resistance.
A battery with emf $\varepsilon=18,\text{V}$ and internal resistance $r=2.0,\Omega$ is connected in series with an external resistor $R=7.0,\Omega$ to form one closed loop. Using the loop rule, what is the potential difference across the battery terminals while the circuit is operating?
18.0 V
1.40 V
4.00 V
14.0 V
Explanation
This question tests AP Physics C concepts of applying Kirchhoff's Loop Rule in circuit analysis. Kirchhoff's Loop Rule states that the algebraic sum of voltage changes around a closed loop must equal zero. In this circuit, a battery with emf ε=18V and internal resistance r=2.0Ω connects to an external resistor R=7.0Ω. Choice A (14.0 V) is correct because the current is I = ε/(R+r) = 18/(7+2) = 2A, making the terminal voltage = ε - Ir = 18 - 2(2) = 14V. Choice B (18.0 V) is incorrect as it ignores the internal resistance voltage drop. To help students: Stress that terminal voltage equals emf minus the internal voltage drop. Practice problems with varying internal resistance values to build intuition.
A battery with emf $\varepsilon=15,\text{V}$ and internal resistance $r=0.50,\Omega$ is connected in series with an external resistor $R=4.5,\Omega$. Using the loop rule, what is the potential difference across the battery terminals during operation?
13.5 V
0.135 V
1.50 V
15.0 V
Explanation
This question tests AP Physics C concepts of applying Kirchhoff's Loop Rule in circuit analysis. Kirchhoff's Loop Rule requires that the sum of all voltage changes around a closed loop equals zero. In this circuit, a battery with emf ε=15V and internal resistance r=0.50Ω connects to external resistor R=4.5Ω. Choice A (13.5 V) is correct because the current is I = ε/(R+r) = 15/(4.5+0.5) = 3A, making terminal voltage = ε - Ir = 15 - 3(0.5) = 13.5V. Choice B (15.0 V) is incorrect as it neglects the internal resistance effect. To help students: Reinforce that terminal voltage is always less than emf when current flows. Practice calculating both current and terminal voltage in circuits with internal resistance.