Subjects circuit analysis

Equivalent Voltage 89E62B

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1. **Problem statement:** Find the equivalent voltage source of the given current source circuit at terminals A-B. Given: - Current source $I_1 = 1A$ with resistor $30\ \Omega$ - Current source $I_2 = 2A$ with resistor $30\ \Omega$ 2. **Formula and rules:** To convert a current source in parallel with a resistor to an equivalent voltage source, use the source transformation formula: $$V = I \times R$$ where $V$ is the voltage of the equivalent voltage source, $I$ is the current of the current source, and $R$ is the resistor in parallel. 3. **Calculate equivalent voltage sources:** For $I_1$ branch: $$V_1 = I_1 \times R = 1 \times 30 = 30\ V$$ For $I_2$ branch: $$V_2 = I_2 \times R = 2 \times 30 = 60\ V$$ 4. **Combine the two voltage sources in series:** Since the two sources are connected at terminals A-B, and assuming they are in series aiding, $$V_{eq} = V_1 + V_2 = 30 + 60 = 90\ V$$ The equivalent resistor is the sum of the two resistors in series: $$R_{eq} = 30 + 30 = 60\ \Omega$$ 5. **Final equivalent voltage source:** $$\boxed{V_{eq} = 90\ V, \quad R_{eq} = 60\ \Omega}$$ --- **Note:** The second question is not solved as per instructions to solve only the first problem.