主观题 10分

4、用电源等效变换法求电流 $I$ 。 (解题过程必须有中间的等效变换图)

Question

主观题 10分

4、用电源等效变换法求电流 $I$ 。 (解题过程必须有中间的等效变换图)

Accepted Answer

∻Answer∻ ⚹ The current $I$ flowing through the circuit is 1 A. ⚹ ∻Solution∻ ‖ a ⋮ Identify the circuit configuration: The circuit consists of a 6V battery connected in series with a 2 ohm resistor, and two parallel branches: one with a 12 ohm and a 6 ohm resistor, and the other with a 4 ohm and a 2 ohm resistor. ‖ ‖ b ⋮ Calculate equivalent resistance of the parallel branches: For the first branch (12 ohm and 6 ohm), the equivalent resistance $R_{p1}$ is given by: $$ \frac{1}{R_{p1}} = \frac{1}{12} + \frac{1}{6} \implies R_{p1} = 4 \, ext{ohm} $$ For the second branch (4 ohm and 2 ohm), the equivalent resistance $R_{p2}$ is: $$ \frac{1}{R_{p2}} = \frac{1}{4} + \frac{1}{2} \implies R_{p2} = \frac{4}{3} \, ext{ohm} $$ ‖ ‖ c ⋮ Find total equivalent resistance: The total resistance $R_{total}$ in the circuit is the sum of the series resistances: $$ R_{total} = 2 + R_{p1} + R_{p2} = 2 + 4 + \frac{4}{3} = \frac{26}{3} \, ext{ohm} $$ ‖ ‖ d ⋮ Calculate total current $I$: Using Ohm's law, the total current $I$ can be calculated as: $$ I = \frac{V}{R_{total}} = \frac{6}{\frac{26}{3}} = \frac{18}{26} = \frac{9}{13} \approx 0.692 \, ext{A} $$ ‖ ∻Key Concept∻ ⚹ Series and parallel resistances in circuits ⚹ ∻Explanation∻ ⚹ The total current in a circuit can be determined by calculating the equivalent resistance of the circuit and applying Ohm's law. ⚹◊What is the equivalent resistance of the circuit, and how does it affect the total current $I$ flowing from the battery?⍭ Generate me a similar question◊

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