A circuit is constructed from two voltage sources (V₁ and V₂) and three resistors (R₁, R₂, and R₃). If the potential of each voltage source is 10 V and the resistance of each resistor is 5 Ω, what is the current exiting Point A?

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Quizplus · Accepted Answer

11ecba2d_1313_ebe0_a3bf_1d7853edba50_MD0008_00 In contrast to simple circuits, complicated circuits are structured such that current flows through two or more loops (ie, closed pathways) sharing only some circuit components. Junctions are points along a complicated circuit at which three or more circuit elements meet. Junctions bridge two or more circuit loops to one another, and the sum of current entering the junction (I_enter) must be equal to the current exiting that junction (I_exit): 11ecba2d_1313_ebe1_a3bf_732b1309c723_MD0008_00 Ienter=Iexit In other words, charge cannot accumulate or disappear at junctions and must pass on to other circuit elements. Furthermore, the total voltage drop (V) within each loop is related to the resistance (R) of and current traveling across all resistors within the loop: 11ecba2d_1314_12f2_a3bf_0391d50ad7e6_MD0008_00 Vn=I1R1+I2R2…+InRn In the prompt, current flows through a complicated circuit with two voltage sources (V₁ and V₂) and three resistors (R₁, R₂, and R₃). Two loops are present within each circuit, the first of which is composed of voltage source V₁ and resistors R₁ and R₃. The second loop is composed of voltage source V₂ and resistors R₂ and R_3. One current unique to each loop (I_A and I_B) enters Point A and another current shared by both loops exits Point A (I_exit): 11ecba2d_1314_12f3_a3bf_0d3a4d22880e_MD0008_00 11ecba2d_1314_12f4_a3bf_79ff5bdfa949_MD0008_00 11ecba2d_1314_12f5_a3bf_edb2be69b773_MD0008_00 The question states that each loop is composed of a 10-V source connected to two resistors, each with a resistance of 5 Ω: 11ecba2d_1314_12f6_a3bf_fd9efc5f131f_MD0008_00 11ecba2d_1314_12f7_a3bf_3dec36b8d600_MD0008_00 11ecba2d_1314_3a08_a3bf_db75c5add4eb_MD0008_00 11ecba2d_1314_3a09_a3bf_23941187c67d_MD0008_00 Because both loops that converge on Point A and are identical, I_exit must be twice the value of I_A and I_B: 11ecba2d_1314_3a0a_a3bf_973bdbd14740_MD0008_00 11ecba2d_1314_3a0b_a3bf_13e1f2736104_MD0008_00 11ecba2d_1314_3a0c_a3bf_79aa5db9ba39_MD0008_00 Consequently, the quantity of current exiting Point A must be 4/3 C/s (Choice C) because charge cannot accumulate or disappear within circuit junctions. Educational objective: Circuits composed of multiple loops contain junctions, points on the circuit at which three or more elements meet. The current entering any junction must be equal to the current exiting the junction.

A Circuit Is Constructed from Two Voltage Sources (V1 and V2)

A Circuit Is Constructed from Two Voltage Sources (V₁ and V₂)