(a) Find the current in each resistor of the circuit shown in the figure by usin
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Question
(a) Find the current in each resistor of the circuit shown in the figure by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoff?s laws: one with the node rule; a second using the loop rule through the battery the 6.0-coulomb resistor, and the 24.0-coulomb resistor; and the third using the loop rule through the 12.0-coulomb and 24.0-coulomb resistors. Solve to check the answers found in part (a).
(a) Find the current in each resistor of the circuit shown in the figure by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoff?s laws: one with the node rule; a second using the loop rule through the battery the 6.0-coulomb resistor, and the 24.0-coulomb resistor; and the third using the loop rule through the 12.0-coulomb and 24.0-coulomb resistors. Solve to check the answers found in part (a).Explanation / Answer
Two resistors are connected in parallel, Hence Req = (R1 * R2)/(R1 + R2) = 12 * 24 / 36 = 8 ohms This equivalent resistance is in series with a 6 ohms resistor, hence total R = 14 ohms. V = IR, Hence, I = 42/14 = 3 A Potential drop across the 6 ohms resistor = 6 * 3 = 18 V Hence, potential drop across the other two = 24 V Hence, I12 = 24/12 = 2 A, and I24 = 24/24 = 1 A For writing Kirchoffs equations, consider independent loops such as , 42 - 3 * 6 - I12 * 12 = 0 42 - 3 * 6 - I24 * 24 = 0 I12 * 12 = I24 * 24 By solving, the answers can be verified
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