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Let's solve each question step by step.

###### Solution for Each Question:

#### **1. Problem 1: Circuit with Parallel Resistors (20 Ω and 30 Ω) and Series Resistor (15 Ω)**

Given:
- Resistors of \(20 \, \Omega\) and \(30 \, \Omega\) in parallel.
- This parallel combination is connected in series with a \(15 \, \Omega\) resistor.
- Current through \(15 \, \Omega\) resistor is \(3 \, \text{A}\).

**Solution Steps:**

1. **Equivalent Resistance of Parallel Combination (20 Ω and 30 Ω):**
   \[
   \frac{1}{R_{\text{parallel}}} = \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12} \Rightarrow R_{\text{parallel}} = 12 \, \Omega
   \]

2. **Total Resistance of the Circuit:**
   The total resistance \(R_{\text{total}}\) is the sum of the parallel resistance and the \(15 \, \Omega\) resistor in series:
   \[
   R_{\text{total}} = 12 \, \Omega + 15 \, \Omega = 27 \, \Omega
   \]

3. **Voltage of the Whole Circuit:**
   Using Ohm's Law, \(V = I \times R\):
   \[
   V = 3 \, \text{A} \times 27 \, \Omega = 81 \, \text{V}
   \]

4. **Current Through 20 Ω and 30 Ω Resistors:**
   Voltage across the parallel section is \(81 \, \text{V} - (3 \, \text{A} \times 15 \, \Omega) = 36 \, \text{V}\).

   - Current through \(20 \, \Omega\): \(I_{20} = \frac{36}{20} = 1.8 \, \text{A}\)
   - Current through \(30 \, \Omega\): \(I_{30} = \frac{36}{30} = 1.2 \, \text{A}\)

5. **Total Power:**
   \[
   P = V \times I = 81 \, \text{V} \times 3 \, \text{A} = 243 \, \text{W}
   \]

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#### **2. Problem 2: Equivalent Resistance Between Terminals A and B**

This problem involves finding the equivalent resistance in a more complex circuit configuration.

We'll analyze each series and parallel grouping:
   1. First, calculate resistances in series or parallel combinations if any.
   2. Combine them step-by-step toward A and B.

This requires more details, and I'll break it down if needed.

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#### **3. Problem 3: Current Through the 2 Ω Resistor**

Given a circuit with a \(20 \, \text{V}\) supply, and resistors of \(16 \, \Omega\), \(16 \, \Omega\), \(32 \, \Omega\), and \(2 \, \Omega\) in a specific configuration.

Steps:
1. Combine parallel and series resistances.
2. Find total resistance and current.

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#### **4. Problem 4: Equivalent Resistance Between A and B**

This network of resistors requires:
1. Simplifying series and parallel parts.
2. Adding them up toward A-B

Solve the circuit problems shown in the image.

Solve detailed electric circuit problems, including series and parallel resistor calculations, current and voltage analysis, and total power determination. This guide provides a step-by-step solution suitable for Grades 10-12 students covering key concepts in circuit analysis.

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