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	What is the equivalent resistance of the three-resistor network?
Req=x (see notes on how to compute the Req of R1 in parallel with R2)

	What is the value of current I1?

I_1=5V/(R3+Req)


	What is the voltage drop over R1?






	What is the voltage drop over R2?






	What is the voltage drop over R3?








	What is the current flowing through R1?





	What is the current flowing through R2?






	What is the current flowing through R3?


Let's go step by step to solve the given circuit.

### 1. **Equivalent Resistance (Req) of R1 in parallel with R2:**
Given:
- \( R_1 = 10 \, \text{k}\Omega \)
- \( R_2 = 100 \, \text{k}\Omega \)

For resistors in parallel, the equivalent resistance (\( R_{eq} \)) is calculated by:

\[
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}
\]

Substituting the values:

\[
\frac{1}{R_{eq}} = \frac{1}{10,000} + \frac{1}{100,000}
\]

Let's calculate \( R_{eq} \).

---

### 2. **Current \( I_1 \):**
Once we calculate \( R_{eq} \), we can find the total current \( I_1 \) using the following formula:

\[
I_1 = \frac{V}{R_3 + R_{eq}}
\]

Where:
- \( V = 5 \, \text{V} \)
- \( R_3 = 10 \, \text{k}\Omega \)

---

### 3. **Voltage Drop over \( R_1 \):**
The voltage drop over \( R_1 \) can be found using Ohm's Law:

\[
V_{R1} = I_{R1} \cdot R_1
\]

---

### 4. **Voltage Drop over \( R_2 \):**
Since \( R_1 \) and \( R_2 \) are in parallel, the voltage across \( R_2 \) will be the same as that across \( R_1 \):

\[
V_{R2} = V_{R1}
\]

---

### 5. **Voltage Drop over \( R_3 \):**
The voltage drop across \( R_3 \) is given by:

\[
V_{R3} = I_1 \cdot R_3
\]

---

### 6. **Current through \( R_1 \):**
Once we have the voltage drop over \( R_1 \), we can calculate the current through \( R_1 \) using:

\[
I_{R1} = \frac{V_{R1}}{R_1}
\]

---

### 7. **Current through \( R_2 \):**
Similarly, the current through \( R_2 \) is:

\[
I_{R2} = \frac{V_{R2}}{R_2}
\]

---

### 8. **Current through \( R_3 \):**
This is the same as \( I_1 \), which is the total current flowing through the circuit.

---

Let me now calculate the values for these steps.Here are the calculated results for the circuit:

1. **Equivalent Resistance (Req)** of \(R_1\) and \(R_2\) in parallel:  
   \[
   R_{eq} = 9090.91 \, \Omega
   \]

2. **Total Current \(I_1\)**:  
   \[
   I_1 = 0.2619 \, \text{mA}
   \]

3. **Voltage Drop over \(R_1\)**:  
   \[
   V_{R1} = 2.381 \, \text{V}
   \]

4. **Voltage Drop over \(R_2\)** (same as \(R_1\) since they are in parallel):  
   \[
   V_{R2} = 2.381 \, \text{V}
   \]

5. **Voltage Drop over \(R_3\)**:  
   \[
   V_{R3} = 2.619 \, \text{V}
   \]

6. **Current through \(R_1\)**:  
   \[
   I_{R1} = 0.2381 \, \text{mA}
   \]

7. **Current through \(R_2\)**:  
   \[
   I_{R2} = 0.0238 \, \text{mA}
   \]

8. **Current through \(R_3\)** (same as \(I_1\)):  
   \[
   I_{R3} = 0.2619 \, \text{mA}
   \]

### Do you have any questions or want further details?

Here are some related questions you could explore:
1. How would the total current change if \(R_1\) was increased?
2. What would happen if \(R_2\) was removed from the circuit?
3. How can the power dissipated in each resistor be calculated?
4. What is the role of \(R_3\) in this circuit?
5. How do different resistor configurations (series vs parallel) affect current distribution?

**Tip**: To simplify parallel resistor networks, always apply the reciprocal rule for resistors in parallel.

What is the equivalent resistance of the three-resistor network? What is the value of current I1? What are the voltage drops and current values over R1, R2, and R3?

Learn how to calculate the equivalent resistance of a network of three resistors, the total current, and voltage drops across R1, R2, and R3. This problem covers essential circuit analysis concepts including Ohm's Law and parallel/series resistance. Perfect for electrical engineering students.

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