Physics Notes: Electrokinetics and Circuit Analysis - Baccalaureate 2014

Problem 6 (Baccalaureate 2014): Electrokinetics Study Notes

• This problem focuses on electrokinetics, specifically circuit analysis involving multiple resistors ($R_1, R_2, R_3, R_4$), a switch ($K$), and a generator with an internal resistance ($r$).
• Reference Year: 2014 Baccalaureate Exam.
• Copyright Reference: CD @2015-2016.

Circuit Parameters and Specifications

• Generator Characteristics:   - Electromotive force (t.e.m.): $E$ (Unknown to be determined).   - Internal resistance: $r = 10\,\Omega$ (Transcript OCR: 102).
• Resistor Values:   - Resistor 1: $R_1 = 4\,\Omega$ (Transcript OCR: 402).   - Resistor 2: $R_2 = 3\,\Omega$ (Transcript OCR: 302).   - Resistor 3: $R_3 = 5\,\Omega$ (Transcript OCR: 502).   - Resistor 4: $R_4 = 10\,\Omega$ (Transcript OCR: 100 2).
• Switch State (Condition 1): Switch $K$ is initially closed.
• Measured Characteristic (Condition 1): When $K$ is closed, the current intensity through resistor $R_1$ is $I_1 = 1.2\,A$.

Part A: Equivalent External Resistance ($K$ Closed)

• Objective: Determine the equivalent resistance of the entire external circuit ($R_e$) when the switch $K$ is in the closed position.
• System Configuration: With $K$ closed, the resistors are connected in a specific network configuration (typically involving series and parallel combinations).
• Result: Based on the circuit analysis and the provided solution key, the equivalent resistance is:   - $R_e = 20\,\Omega$

Part B: Electromotive Force ($E$) of the Generator

• Objective: Calculate the total electromotive force ($E$) of the power source.
• Fundamental Principle: Ohm's Law for the entire circuit is applied using the formula:   - $E = I \times (R_e + r)$
• Calculation Context: Since $I_1 = 1.2\,A$ represents the total current delivered by the generator (assuming $R_1$ is in the main branch):   - $E = 1.2\,A \times (20\,\Omega + 10\,\Omega)$   - $E = 1.2\,A \times 30\,\Omega$
• Result:   - $E = 36\,V$

Part C: Current Intensity through Resistor $R_2$

• Objective: Find the current ($I_2$) flowing through the second resistor when the switch $K$ is closed.
• Mechanism: The total current ($I$) from the main branch splits into different parallel branches of the circuit. The intensity through a specific branch is determined by the potential difference across it and its individual resistance.
• Result:   - $I_2 = 1\,A$

Part D: Voltage across Resistor $R_4$ with Open Switch

• Objective: Calculate the terminal voltage ($U$) for resistor $R_4$ when the switch $K$ is open.
• Impact of Opening Switch $K$: Opening the switch changes the topology of the circuit. One branch of the circuit is disconnected, which alters the total equivalent resistance ($R_e'$) and consequently changes the total current ($I'$) and the distribution of voltages across the remaining resistors.
• Analytical Change: With $K$ open, the current through the circuit must be recalculated before applying Ohm's Law to resistor $R_4$ ($U_4 = I_4 \times R_4$).
• Result:   - $U_2$ (represented as the voltage in the second state or for the specific resistor) $= 4.1\,V$

Final Solution Key Summary

• a. Equivalent Resistance ($R_e$): $20\,\Omega$ (Note: Transcript label 290 is a typo for 20).
• b. Electromotive Force ($E$): $36\,V$.
• c. Current through $R_2$ ($I_2$): $1\,A$.
• d. Voltage across resistor ($U$): $4.1\,V$.