A circuit consisting of three ideal batteries with voltages 81, 82, and 83, and three ideal resistors with resistances R1. R2. and R3. is shown in the figure. Calculate the current Ip through point P. Let the sign of the current correspond to its direction, with "up" being positive. 81 = 23.5 V, 82 = 16.5 V, 83 = 31.5 V R1 R = 2.50 k2, R, = 12.5 k2, R3 = 7.75 kQ Ip = mA ww

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A circuit consisting of three ideal batteries with voltages \( \mathcal{E}_1 \), \( \mathcal{E}_2 \), and \( \mathcal{E}_3 \), and three ideal resistors with resistances \( R_1 \), \( R_2 \), and \( R_3 \), is shown in the figure. Calculate the current \( I_P \) through point P. Let the sign of the current correspond to its direction, with "up" being positive.

- \( \mathcal{E}_1 = 23.5 \, \text{V} \), \( \mathcal{E}_2 = 16.5 \, \text{V} \), \( \mathcal{E}_3 = 31.5 \, \text{V} \)

- \( R_1 = 2.50 \, \text{k}\Omega \), \( R_2 = 12.5 \, \text{k}\Omega \), \( R_3 = 7.75 \, \text{k}\Omega \)

\[ I_P = \, \boxed{\phantom{0}} \, \text{mA} \]

**Diagram Explanation:**

The diagram shows three batteries and three resistors connected in a complex circuit. 

- Battery \( \mathcal{E}_1 \) is connected in series with resistor \( R_1 \).
- Battery \( \mathcal{E}_2 \) is in parallel with resistor \( R_3 \), forming a loop with battery \( \mathcal{E}_1 \).
- Battery \( \mathcal{E}_3 \) is connected in series with resistor \( R_2 \) and joins with the parallel combination of \( \mathcal{E}_2 \) and \( R_3 \).
- The point P is located between \( R_1 \) and \( R_2 \) within the circuit, and the current \( I_P \) is to be calculated.

The goal is to determine \( I_P \), the current flowing through point P, using the given values and circuit configuration.
Transcribed Image Text:A circuit consisting of three ideal batteries with voltages \( \mathcal{E}_1 \), \( \mathcal{E}_2 \), and \( \mathcal{E}_3 \), and three ideal resistors with resistances \( R_1 \), \( R_2 \), and \( R_3 \), is shown in the figure. Calculate the current \( I_P \) through point P. Let the sign of the current correspond to its direction, with "up" being positive. - \( \mathcal{E}_1 = 23.5 \, \text{V} \), \( \mathcal{E}_2 = 16.5 \, \text{V} \), \( \mathcal{E}_3 = 31.5 \, \text{V} \) - \( R_1 = 2.50 \, \text{k}\Omega \), \( R_2 = 12.5 \, \text{k}\Omega \), \( R_3 = 7.75 \, \text{k}\Omega \) \[ I_P = \, \boxed{\phantom{0}} \, \text{mA} \] **Diagram Explanation:** The diagram shows three batteries and three resistors connected in a complex circuit. - Battery \( \mathcal{E}_1 \) is connected in series with resistor \( R_1 \). - Battery \( \mathcal{E}_2 \) is in parallel with resistor \( R_3 \), forming a loop with battery \( \mathcal{E}_1 \). - Battery \( \mathcal{E}_3 \) is connected in series with resistor \( R_2 \) and joins with the parallel combination of \( \mathcal{E}_2 \) and \( R_3 \). - The point P is located between \( R_1 \) and \( R_2 \) within the circuit, and the current \( I_P \) is to be calculated. The goal is to determine \( I_P \), the current flowing through point P, using the given values and circuit configuration.
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