Given a 46.0-V battery and 24.0 - Q and 97.0 - Q resistors, find the current when connected in parallel.

College Physics
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ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter21: Circuits And Dc Instruments
Section: Chapter Questions
Problem 79PE: Construe! Your Own Problem Consider a rechargeable lithium cell that is to be used to power a...
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**Problem Statement:**

Given a 46.0-V battery and 24.0-Ω and 97.0-Ω resistors, find the current when connected in parallel.

**Task:**

Provide the solution: ________ A

**Solution Steps:**
1. **Understand the Problem:**
   - A 46.0-volt battery is connected to two resistors in parallel: one with a resistance of 24.0 ohms and the other with a resistance of 97.0 ohms.

2. **Calculate the Total Resistance:**
   - In a parallel circuit, the total resistance \( R_t \) can be calculated using the formula:
     \[
     \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2}
     \]
   - For \( R_1 = 24.0 \, \Omega \) and \( R_2 = 97.0 \, \Omega \), the calculation becomes:
     \[
     \frac{1}{R_t} = \frac{1}{24} + \frac{1}{97}
     \]
   - Solve for \( R_t \).

3. **Calculate the Total Current:**
   - Use Ohm's Law to find the current \( I \) using the formula:
     \[
     I = \frac{V}{R_t}
     \]
   - Where \( V = 46.0 \, \text{V} \).

4. **Provide the Numerical Solution:**
   - Plug in the values and calculate the result to find the current in amperes.
Transcribed Image Text:**Problem Statement:** Given a 46.0-V battery and 24.0-Ω and 97.0-Ω resistors, find the current when connected in parallel. **Task:** Provide the solution: ________ A **Solution Steps:** 1. **Understand the Problem:** - A 46.0-volt battery is connected to two resistors in parallel: one with a resistance of 24.0 ohms and the other with a resistance of 97.0 ohms. 2. **Calculate the Total Resistance:** - In a parallel circuit, the total resistance \( R_t \) can be calculated using the formula: \[ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} \] - For \( R_1 = 24.0 \, \Omega \) and \( R_2 = 97.0 \, \Omega \), the calculation becomes: \[ \frac{1}{R_t} = \frac{1}{24} + \frac{1}{97} \] - Solve for \( R_t \). 3. **Calculate the Total Current:** - Use Ohm's Law to find the current \( I \) using the formula: \[ I = \frac{V}{R_t} \] - Where \( V = 46.0 \, \text{V} \). 4. **Provide the Numerical Solution:** - Plug in the values and calculate the result to find the current in amperes.
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