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The value of the voltage source V(in V) which causes the current I1 to be zero for the circuit shown is

To find the value of voltage \( V \) that causes \( I_1 = 0 \), we can use Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) on the circuit. Let's proceed step by step.

### Step 1: Identify the circuit loops
We have three loops in the circuit, corresponding to the currents:
- \( I_1 \): The loop containing the 20 V source and the 6Ω resistor.
- \( I_2 \): The loop containing the 2Ω, 3Ω, and 1Ω resistors.
- \( I_3 \): The loop with the \( V \) source, 5Ω resistor, and 1Ω resistor (shared with loop 2).

### Step 2: Write KVL equations for each loop
#### Loop 1 (top left loop with \( I_1 \)):
Since \( I_1 = 0 \), there is no current through the 6Ω resistor or the 2Ω resistor. Hence, we don’t need a full equation for this loop.

#### Loop 2 (top right loop with \( I_2 \)):
For this loop, applying KVL:
\[
- I_2(2 + 1) + (I_2 - I_3)(1) = 0
\]
Simplifying:
\[
I_2(3) - I_3(1) = 0 \quad \Rightarrow \quad 3I_2 = I_3
\]
Thus, \( I_3 = 3I_2 \).

#### Loop 3 (bottom loop with \( I_3 \)):
For this loop, applying KVL:
\[
- V + I_3(5) + (I_3 - I_2)(1) = 0
\]
Simplifying:
\[
- V + 5I_3 + (I_3 - I_2) = 0 \quad \Rightarrow \quad - V + 6I_3 - I_2 = 0
\]

### Step 3: Substitute values
Using the relation \( I_3 = 3I_2 \) from Loop 2 into the Loop 3 equation:
\[
- V + 6(3I_2) - I_2 = 0 \quad \Rightarrow \quad - V + 18I_2 - I_2 = 0 \quad \Rightarrow \quad - V + 17I_2 = 0
\]
Thus:
\[
V = 17I_2
\]

### Step 4: Apply the condition \( I_1 = 0 \)
Since \( I_1 = 0 \), it means no current flows through the 6Ω resistor, and the entire circuit reduces to a system with \( I_2 \) and \( I_3 \).

### Step 5: Conclusion
The voltage \( V \) is directly proportional to \( I_2 \), and the value of \( V \) for the given condition is \( V = 17I_2 \). However, to get an exact numerical value of \( V \), we would need additional conditions like the value of \( I_2 \). Based on the circuit configuration, you'd typically solve for the exact values numerically if more data were provided, but the equation \( V = 17I_2 \) holds.

The value of the voltage source V (in V) which causes the current I1 to be zero for the circuit shown is

Find the voltage source V that causes the current I1 to be zero in a circuit using Kirchhoff's Voltage and Current Laws. Step-by-step analysis of the loop equations and voltage calculation provided. Suitable for electrical engineering students.

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