Kirchhoff's Loop Rule - AP Physics 2

1. Find the missing voltage if the loop sum must be zero: $V_1 = 6 \text{V}$, $V_2 = 4 \text{V}$.

   $V_3 = -10 \text{V}$. Loop sum must be zero: $V_3 = 0 - 6 - 4 = -10\text{V}$.

2. What does the loop rule imply for a series circuit?

   Sum of voltage drops equals source voltage. Consequence of Kirchhoff's Loop Rule in series circuits.

3. State the formula for Kirchhoff's Loop Rule.

   $\text{Sum of } V = 0$ for a closed loop. Mathematical expression of Kirchhoff's Loop Rule.

4. What is the voltage across an ideal inductor in a steady-state DC circuit?

   Zero. No voltage drop when current is constant.

5. In a loop with a $10 \text{V}$ battery and $7 \text{V}$, $2 \text{V}$ drops, find missing voltage.

   $1 \text{V}$. Missing voltage: $10 - 7 - 2 = 1\text{V}$.

6. Calculate $V_3$: $V_1 = 8 \text{V}$, $V_2 = 1 \text{V}$, total $= 10 \text{V}$.

   $V_3 = 1 \text{V}$. $V_3 = 10 - 8 - 1 = 1\text{V}$.

7. State Kirchhoff's Loop Rule in terms of electromotive force and potential difference.

   $\text{emf} - \text{sum of } V = 0$. Alternative form emphasizing source and load voltages.

8. What is the potential change in a loop with a $5 \text{V}$ battery and $5 \text{V}$ drop?

   Zero. Voltage gain equals voltage drop, net change is zero.

9. In a loop with two batteries, how do you determine the net emf?

   Add emfs algebraically considering direction. Consider polarity when combining multiple voltage sources.

10. How does Kirchhoff's Loop Rule apply to AC circuits?

    It applies to instantaneous voltages. Rule applies at each instant in time.

11. Calculate the total voltage in a loop with $10 \text{V}$ gain and $10 \text{V}$ drop.

    Zero. Voltage gain equals voltage drop, net is zero.

12. Which physical quantity is conserved according to Kirchhoff's Loop Rule?

    Energy. Electric potential energy is conserved around closed loops.

13. Find the error: Loop equation $3 \text{V} + 4 \text{V} = 8 \text{V}$.

    Correct: $3 \text{V} + 4 \text{V} = 7 \text{V}$. Addition error: $3 + 4 = 7$, not $8$.

14. What role do resistors play in Kirchhoff's Loop Rule?

    Contribute voltage drops. Current through resistance creates voltage drop.

15. How are resistances considered in Kirchhoff's Loop Rule?

    As potential drops. Voltage drops according to Ohm's law.

16. Solve for $V_3$: $V_1 = 7 \text{V}$, $V_2 = 2 \text{V}$, total $= 10 \text{V}$.

    $V_3 = 1 \text{V}$. $V_3 = 10 - 7 - 2 = 1\text{V}$.

17. Identify the error: Loop equation $10 \text{V} - 5 \text{V} = 6 \text{V}$.

    Correct: $10 \text{V} - 5 \text{V} = 5 \text{V}$. Basic subtraction error: $10 - 5 = 5$, not $6$.

18. What is Kirchhoff's Loop Rule?

    The total voltage around a closed loop is zero. Based on conservation of energy in electric circuits.

19. If a loop has a $15 \text{V}$ battery and $5 \text{V}$, $3 \text{V}$ drops, what is the remaining drop?

    $7 \text{V}$. Remaining drop: $15 - 5 - 3 = 7\text{V}$.

20. What must the sum of potential differences in a closed circuit equal?

    Zero. Follows from conservation of energy principle.

21. What does Kirchhoff's Loop Rule say about net emf and potential difference in a loop?

    They must sum to zero. Energy conservation requires zero net potential change.

22. What sign is assigned to a voltage gain in a loop equation?

    Positive. Voltage sources increase electric potential.

23. Identify the loop equation for a $6 \text{V}$ battery and $2 \text{V}$, $4 \text{V}$ drops.

    $6 \text{V} - 2 \text{V} - 4 \text{V} = 0$. Battery voltage equals sum of resistor drops.

24. What happens to total potential in a loop with equal voltage gains and drops?

    It remains zero. Gains and drops cancel each other out.

25. In a loop with $12 \text{V}$ gain, $4 \text{V}$ drop, find the remaining voltage drop.

    $8 \text{V}$. Remaining drop: $12 - 4 = 8\text{V}$.

26. What sign is assigned to a voltage drop in a loop equation?

    Negative. Resistors decrease electric potential.

27. How is Kirchhoff's Loop Rule used in mesh analysis?

    To set up equations for unknown currents. Creates system of equations for circuit analysis.

28. What is the loop equation for a circuit with $9 \text{V}$ battery and $1 \text{V}$, $8 \text{V}$ drops?

    $9 \text{V} - 1 \text{V} - 8 \text{V} = 0$. Shows battery voltage equals sum of voltage drops.

29. What is the value of missing voltage if loop sum is zero: $V_1 = 5 \text{V}$, $V_2 = 7 \text{V}$?

    $V_3 = -12 \text{V}$. For zero sum: $V_3 = 0 - 5 - 7 = -12\text{V}$.

30. Identify the equation representing Kirchhoff's Loop Rule.

    $\text{Sum of } V = 0$. Mathematical statement of the loop rule.

31. Which principle is Kirchhoff's Loop Rule based on?

    Conservation of energy. Energy cannot be created or destroyed in circuits.

32. What is Kirchhoff's Loop Rule used for in electrical circuits?

    Analyzing voltage distribution. Determines how voltage is distributed in circuits.

33. Which component's voltage is considered positive in the loop equation?

    Battery in the direction of emf. EMF increases potential when traversed from negative to positive terminal.

34. In Kirchhoff's Loop Rule, what is the net change in electric potential?

    Zero. Starting and ending at same point yields zero net change.

35. What is the purpose of Kirchhoff's Loop Rule in circuit analysis?

    To ensure energy conservation. Maintains energy conservation in electrical systems.

36. What is the voltage across an ideal capacitor in a steady-state DC circuit?

    Constant. Capacitor maintains fixed voltage in DC steady state.

37. In Kirchhoff's Loop Rule, what is the sum of emfs and potential drops in a loop?

    Zero. Consequence of energy conservation principle.

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