An engineer built the circuit depicted in the figure. Assuming & = 7.60 V and R = 4.70 02, find the following quantities. 12.0 V a E 2.00 Ω ww www R 4.00 Ω b (a) the current in the 2.000 resistor (Enter the magnitude in mA.) 718.232 mA (b) the potential difference (in V) between points a and b VbV₂ = -3.8453 X Apply Ohm's law and your result from part (a) to calculate your answer. It might help to redraw the circuit so that points a and h are clearly defined junctions V

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### Educational Circuit Analysis

An engineer built the circuit depicted in the figure. Assuming \( \mathcal{E} = 7.60 \, \text{V} \) and \( R = 4.70 \, \Omega \), find the following quantities.

#### Diagram Explanation
The circuit consists of:
- A battery with a voltage of 12.0 V.
- Two resistors in series: 
  - One with a resistance of 2.00 Ω.
  - Another with a resistance of 4.00 Ω.
- A third resistor, labeled \( R \), with a resistance of 4.70 Ω in parallel to the battery.
- Points a and b are labeled as junction points in the circuit.

#### Quantities to Find

**(a) The current in the 2.00 Ω resistor**

- Result: **718.232 mA**

The text provides the calculated current in the 2.00 Ω resistor, marked correctly.

**(b) The potential difference (in V) between points a and b**

- Expression: \( V_b - V_a = -3.8453 \) (Calculated incorrectly)

The text advises applying Ohm's law and using the result from part (a) to calculate the correct answer. It suggests redrawing the circuit to ensure points a and b are clearly defined.

#### Notes
For further understanding, apply the principles of Ohm's Law, which states \( V = IR \), to analyze how the potential difference and current behave in this circuit setup.

### Need Help?
For detailed explanations and help, you can click on "Read It" for additional resources.

---
> **Note:** This educational content helps in understanding fundamental circuit analysis, involving series and parallel resistors, and application of Ohm's Law.
Transcribed Image Text:### Educational Circuit Analysis An engineer built the circuit depicted in the figure. Assuming \( \mathcal{E} = 7.60 \, \text{V} \) and \( R = 4.70 \, \Omega \), find the following quantities. #### Diagram Explanation The circuit consists of: - A battery with a voltage of 12.0 V. - Two resistors in series: - One with a resistance of 2.00 Ω. - Another with a resistance of 4.00 Ω. - A third resistor, labeled \( R \), with a resistance of 4.70 Ω in parallel to the battery. - Points a and b are labeled as junction points in the circuit. #### Quantities to Find **(a) The current in the 2.00 Ω resistor** - Result: **718.232 mA** The text provides the calculated current in the 2.00 Ω resistor, marked correctly. **(b) The potential difference (in V) between points a and b** - Expression: \( V_b - V_a = -3.8453 \) (Calculated incorrectly) The text advises applying Ohm's law and using the result from part (a) to calculate the correct answer. It suggests redrawing the circuit to ensure points a and b are clearly defined. #### Notes For further understanding, apply the principles of Ohm's Law, which states \( V = IR \), to analyze how the potential difference and current behave in this circuit setup. ### Need Help? For detailed explanations and help, you can click on "Read It" for additional resources. --- > **Note:** This educational content helps in understanding fundamental circuit analysis, involving series and parallel resistors, and application of Ohm's Law.
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