Question

The current I supplied by the DC voltage source in the circuit shown in the figure is ______

• A. zero
• B. $0.5\text{ A}$
• C. $1\text{ A}$
• D. $2\text{ A}$

Hint:

An ideal current source in parallel with a resistor can satisfy the resistor's current demand entirely if their values match.
In this case, the $1\text{ A}$ source supplies exactly what the $1\ \Omega$ resistor needs at $1\text{ V}$, leaving zero net current for the voltage source to supply.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem asks for the current $I$ supplied by the $1\text{ V}$ DC voltage source.
The circuit has a $1\text{ V}$ DC source in parallel with a $1\ \Omega$ resistor and a $1\text{ A}$ independent current source.

Step 2: Key Formula or Approach:
We will apply Kirchhoff's Current Law (KCL) at the top node of the parallel network.
The voltage at the top node is fixed at $1\text{ V}$ due to the ideal voltage source connected in parallel.

Step 3: Detailed Explanation:

• Let the bottom wire be the reference node (Ground, $0\text{ V}$).

• The top node voltage is fixed at $V_{node} = 1\text{ V}$.

• The current flowing downwards through the middle branch resistor of $1\ \Omega$ is:
\[ I_{resistor} = \frac{V_{node}}{1\ \Omega} = \frac{1\text{ V}}{1\ \Omega} = 1\text{ A} \]

• The current source in the rightmost branch is forcing a constant current of $1\text{ A}$ upwards into the top node.

• Let $I$ be the current supplied by the $1\text{ V}$ voltage source (leaving its positive terminal into the top node).

• Applying KCL at the top node:
\[ \sum I_{entering} = \sum I_{leaving} \]
\[ I + 1\text{ A (from current source)} = I_{resistor} \]
\[ I + 1 = 1 \]
\[ I = 0\text{ A} \]

Step 4: Final Answer:
The current supplied by the voltage source is zero, which corresponds to Option (A).