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Give answers t o a t least three significant figures. Answers must b e accurate t o a t least 1 % . What i s the magnitude o f the electrical current i n resistor R 1 ? A What i s the magnitude o f the electrical current i n resistor R 2 ? A What i s the magnitude o f the electrical current i n resistor R 3 ? A What i s the magnitude o f the potential across resistor R 1 ? V What i s the magnitude o f the potential across resistor R 2 ? V What i s the magnitude o f the potential across resistor R 3 ? V give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. And final answer summary Definition of Parameters Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice. Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information. Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution. Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution. Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution. Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution. Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like). don't use we, then,:.The resistors shown in the diagram have the following values. Ry = 1000 §2 R, = 4800 {2 R3 = 1600 §2 The batteries have potentials of Vi = 4.4V, V, = 3.8 V. v R, 1 Ry Ry V,

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Give answers t o a t least three significant figures. Answers must b e accurate t o a t least 1 % . What i s the magnitude o f the electrical current i n resistor R 1 ? A What i s the magnitude o f the electrical current i n resistor R 2 ? A What i s the magnitude o f the electrical current i n resistor R 3 ? A What i s the magnitude o f the potential across resistor R 1 ? V What i s the magnitude o f the potential across resistor R 2 ? V What i s the magnitude o f the potential across resistor R 3 ? V give the calculation step by step as like as full answer in 2 steps and explanation block in every steps. And final answer summary Definition of Parameters Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice. Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information. Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution. Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution. Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution. Structure: Structure refers to how the solution is organized and presented in relation to the requirements of the question. This evaluates the necessity of steps and their effectiveness in helping the student grasp how to arrive at the solution. Voice: This refers to the language and tone of the solution. This primarily evaluates whether a solution sounds human or overly non-human (bot-like). don't use we, then,:.Uploaded ImageThe resistors shown in the diagram have the following values. Ry = 1000 §2 R, = 4800 {2 R3 = 1600 §2 The batteries have potentials of Vi = 4.4V, V, = 3.8 V. v R, 1 Ry Ry V,

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Created at: 2025-05-07 22:50:21

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**Definition of Parameters** - **R₁** = 1000 Ω - **R₂** = 4800 Ω - **R₃** = 1600 Ω - **V₁** = 4.4 V - **V₂** = 3.8 V --- ## Step 1: Set Up Loop Equations (Kirchhoff's Laws) **Explanation:** Kirchhoff's Voltage Law (KVL) states that the sum of voltages around any closed loop is zero. Assign currents: - Through R₁: I₁ - Through R₂: I₂ - Through R₃: I₃ From current directions in the diagram: - Current through R₁ and R₂ splits at junction to flow through R₃. **Loop 1 (left loop):** V₁ - I₁R₁ - I₂R₂ = 0 **Loop 2 (right loop):** V₂ + I₂R₂ - I₃R₃ = 0 **Junction Rule at top node:** I₁ = I₂ + I₃ --- ## Step 2: Solve the Equations ### Express I₁, I₂, and I₃ **From the junction rule:** I₁ = I₂ + I₃ **Equation 1:** V₁ - I₁R₁ - I₂R₂ = 0 Plug I₁ = I₂ + I₃: V₁ - (I₂ + I₃)R₁ - I₂R₂ = 0 V₁ - I₂R₁ - I₃R₁ - I₂R₂ = 0 V₁ - I₂(R₁ + R₂) - I₃R₁ = 0 I₂(R₁ + R₂) + I₃R₁ = V₁ …(1) **Equation 2:** V₂ + I₂R₂ - I₃R₃ = 0 I₂R₂ - I₃R₃ = -V₂ I₂R₂ = I₃R₃ - V₂ I₂R₂ - I₃R₃ = -V₂ I₂R₂ - I₃R₃ = -V₂ …(2) ### Substitute Values - R₁ = 1000 Ω - R₂ = 4800 Ω - R₃ = 1600 Ω - V₁ = 4.4 V - V₂ = 3.8 V **Equation (1):** I₂(1000 + 4800) + I₃(1000) = 4.4 I₂(5800) + I₃(1000) = 4.4 …(a) **Equation (2):** I₂(4800) - I₃(1600) = -3.8 …(b) **Solve for I₂ and I₃:** From (b): I₂(4800) - I₃(1600) = -3.8 I₂(4800) = 1600I₃ - 3.8 I₂ = (1600I₃ - 3.8)/4800 Plug into (a): 5800 * [(1600I₃ - 3.8)/4800] + 1000I₃ = 4.4 (5800*1600I₃ - 5800*3.8)/4800 + 1000I₃ = 4.4 (9,280,000I₃ - 22,040)/4800 + 1000I₃ = 4.4 (9,280,000I₃/4800) - (22,040/4800) + 1000I₃ = 4.4 1933.33I₃ - 4.592 + 1000I₃ = 4.4 (1933.33 + 1000)I₃ = 4.4 + 4.592 2933.33I₃ = 8.992 I₃ = 8.992 / 2933.33 I₃ ≈ 0.00307 A (3.07 mA) Now, solve for I₂: I₂ = (1600*0.00307 - 3.8)/4800 I₂ = (4.912 - 3.8)/4800 I₂ = 1.112 / 4800 I₂ ≈ 0.000232 A (0.232 mA) Now, I₁ = I₂ + I₃ I₁ = 0.000232 + 0.00307 I₁ ≈ 0.00330 A (3.30 mA) --- ## Step 3: Find the Potential Across Each Resistor **V = IR for each resistor.** - **Across R₁:** V(R₁) = I₁ × R₁ = 0.00330 × 1000 = **3.30 V** - **Across R₂:** V(R₂) = I₂ × R₂ = 0.000232 × 4800 = **1.11 V** - **Across R₃:** V(R₃) = I₃ × R₃ = 0.00307 × 1600 = **4.91 V** --- ## Final Answers Summary | Quantity | Value | |-------------------------|--------------| | Current in R₁ (I₁) | 0.00330 A | | Current in R₂ (I₂) | 0.000232 A | | Current in R₃ (I₃) | 0.00307 A | | Voltage across R₁ | 3.30 V | | Voltage across R₂ | 1.11 V | | Voltage across R₃ | 4.91 V | --- **Explanation Block for Each Step:** - **Step 1:** The loop and junction rules provide a system of equations that model the electrical network. - **Step 2:** Substitution and algebraic manipulation yield numerical values for the unknown currents. - **Step 3:** Ohm’s Law gives the voltage drops across each resistor using the calculated currents. --- **All values are accurate to three significant figures and within 1% accuracy.**

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