AP Physics 1 Questions: Internal Resistance and Circuit Analysis

📚 Quick Study Guide

• 🔋 Internal Resistance (r): Real batteries have internal resistance, which reduces the terminal voltage when current flows.
• 📐 Terminal Voltage (V_terminal): $V_{terminal} = \mathcal{E} - Ir$, where $\mathcal{E}$ is the EMF and $I$ is the current.
• 🔄 EMF ($\mathcal{E}$): The electromotive force is the total voltage provided by the battery.
• 💡 Circuit Analysis: Use Kirchhoff's laws to analyze circuits with internal resistance.
• ⚖️ Ohm's Law: Remember Ohm's Law: $V = IR$
• 🔌 Power Dissipation: Power dissipated in the internal resistance is $P = I^2r$.

🧪 Practice Quiz

1. Which of the following statements is true regarding the terminal voltage of a real battery?
   1. A) It is always equal to the EMF of the battery.
   2. B) It is always greater than the EMF of the battery.
   3. C) It is equal to the EMF minus the voltage drop across the internal resistance.
   4. D) It is always zero.
2. A battery with an EMF of 12 V has an internal resistance of 0.5 $\Omega$. What is the terminal voltage when a current of 2 A is flowing through the battery?
   1. A) 13 V
   2. B) 11 V
   3. C) 24 V
   4. D) 6 V
3. In a circuit with a battery and a resistor, how does the internal resistance of the battery affect the current in the circuit?
   1. A) It increases the current.
   2. B) It decreases the current.
   3. C) It has no effect on the current.
   4. D) It doubles the current.
4. A battery with an internal resistance of 1 $\Omega$ is connected to a 5 $\Omega$ resistor. If the EMF of the battery is 6 V, what is the current flowing through the circuit?
   1. A) 0.5 A
   2. B) 1 A
   3. C) 6 A
   4. D) 1.2 A
5. What happens to the power dissipated in the internal resistance of a battery as the current flowing through it increases?
   1. A) It decreases.
   2. B) It increases.
   3. C) It remains constant.
   4. D) It becomes zero.
6. A 9V battery has an internal resistance of 0.2$\Omega$. What is the power dissipated by the internal resistance when delivering a current of 1.5A?
   1. A) 0.3 W
   2. B) 0.45 W
   3. C) 0.9 W
   4. D) 1.8 W
7. A battery is short-circuited (connected directly to itself). If the EMF is $\mathcal{E}$ and the internal resistance is r, what is the current flowing through the battery?
   1. A) 0
   2. B) $\mathcal{E}$
   3. C) $\mathcal{E}$/r
   4. D) r/$\mathcal{E}$