Two batteries with emf E, and E,, with internal resistances r, and r, respectively, are connected as shown in the diagram below. (Assume E, = 12 V and r, = 1 N.) (a) Calculate the magnitude and indicate the direction of flow of current in the figure shown above. E, = 31.0 V and r, = 0.35 N. magnitude direction counterclockwise (b) Find the terminal voltage of each battery. Vっ
Two batteries with emf E, and E,, with internal resistances r, and r, respectively, are connected as shown in the diagram below. (Assume E, = 12 V and r, = 1 N.) (a) Calculate the magnitude and indicate the direction of flow of current in the figure shown above. E, = 31.0 V and r, = 0.35 N. magnitude direction counterclockwise (b) Find the terminal voltage of each battery. Vっ
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You and a group of friends are on a day trip to a nearby national park. After a fun-filled day of fishing and boating, you are ready to head back home when you find that your car battery is dead. Your friend offers to use his car's battery and jumper cables to charge yours. The connections are shown in the two diagrams below. The internal resistance of your car battery is \( r_d = 3.15 \, \Omega \), that of your friend's battery is \( r_L = 0.01 \, \Omega \), and that of the starter is \( r_s = 0.07 \, \Omega \). The live battery has a voltage of 12.0 V and the dead battery in your car has a voltage of 10.0 V. What are the currents through the starter and the dead battery? (Enter your answer for \( I_s \) to at least one decimal place.)
\( I_s = \boxed{150.0283142} \, \text{A} \)
\( I_d = \boxed{0.563612266} \, \text{A} \)
*Use your value for \( I_s \) to find the current through the dead battery.*
**Diagrams:**
1. **Left Diagram**:
- Shows the connections between a live battery, a dead battery, a starter, and an ignition switch.
- The live and dead batteries are connected in parallel, both supplying current to the starter.
2. **Right Diagram**:
- Contains a series circuit including three resistors: \( r_L \) (live battery resistance), \( r_d \) (dead battery resistance), and \( r_s \) (starter resistance).
- \( \varepsilon_L \) denotes the voltage of the live battery (12.0 V), and \( \varepsilon_d \) denotes the voltage of the dead battery (10.0 V).
- The live battery is connected in series with an internal resistance \( r_L \) and the dead battery with \( r_d \), both encountering the starter resistance \( r_s \).
This setup helps in understanding how jumper cables function in assisting a dead battery, focusing on the current distribution in the circuit components.
Transcribed Image Text:**Title: Analyzing a Circuit with Two Batteries**
**Overview:**
This educational module focuses on understanding a circuit that includes two batteries with different electromotive forces (emfs) and internal resistances. The problem involves calculating current flow and terminal voltages.
**Circuit Description:**
- **Components:**
- Two batteries: \( \mathcal{E}_1 \) and \( \mathcal{E}_2 \)
- Internal resistances: \( r_1 \) and \( r_2 \)
- **Parameters:**
- \( \mathcal{E}_1 = 12 \, \text{V} \)
- \( r_1 = 1 \, \Omega \)
- \( \mathcal{E}_2 = 31.0 \, \text{V} \)
- \( r_2 = 0.35 \, \Omega \)
**Tasks:**
1. **Calculate Current:**
- **Magnitude and Direction:**
- Determine the current's magnitude in Amperes and its direction (clockwise or counterclockwise) for the entire circuit.
2. **Find Terminal Voltages:**
- **Determine \( V_1 \) and \( V_2 \):**
- Calculate the terminal voltages of each battery:
- \( V_1 \) (voltage across \( \mathcal{E}_1 \))
- \( V_2 \) (voltage across \( \mathcal{E}_2 \))
**Diagram Explanation:**
The circuit diagram consists of two loops with series-connected batteries. Each battery is represented with its emf (a source of voltage) and a resistor symbol representing internal resistance. The loop suggests a directional flow for current analysis.
Understanding the circuit configuration will allow us to apply Kirchhoff’s laws to find the solution.
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