In the circuit shown below, the current through the inductor (in A) is
Show Hint
When a circuit diagram is ambiguous but the options suggest a simple answer, try to find the most straightforward interpretation. In bridge circuits, calculate the current in a branch by dividing the voltage across that branch by the branch's total impedance.
Step 1: Interpret the complex circuit diagram.
The diagram shows a Wheatstone bridge configuration. The symbols for sources inside the diagram are confusing. A common simplification for such problems is to assume a single excitation source across the main terminals of the bridge and that the internal symbols are for reference. Let's assume the bridge is excited by a 1V source connected between the top and bottom nodes. The inductor with impedance \(j\Omega\) is in the top-right arm of the bridge.
Step 2: Analyze the bridge under this assumption.
Let the top node be A and the bottom node be B, so \(V_{AB} = 1V\).
The bridge has two parallel branches connected across A and B.
Branch 1 (left side): A \(1\Omega\) resistor in series with a \(-j\Omega\) capacitor. Total impedance \(Z_{left} = 1 - j\Omega\).
Branch 2 (right side): A \(1\Omega\) resistor in series with the \(j\Omega\) inductor. Total impedance \(Z_{right} = 1 + j\Omega\).
The question asks for the current through the inductor, which is the current flowing through Branch 2.
Step 3: Calculate the current through the inductor's branch.
Using Ohm's law, the current \(I_{inductor}\) flowing through the right branch is the voltage across the branch divided by the impedance of the branch.
\[
I_{inductor} = \frac{V_{AB}}{Z_{right}}
\]
Substituting the values:
\[
I_{inductor} = \frac{1V}{1 + j\Omega} = \frac{1}{1+j} \, A
\]
This result matches one of the options.
Alternative Interpretation (Bridge Balance):
Let's check if the bridge is balanced. The arms are \(Z_1=1, Z_2=j, Z_3=-j, Z_4=1\). The balance condition is \(Z_1 Z_4 = Z_2 Z_3\).
\(1 \times 1 = 1\).
\(j \times (-j) = -j^2 = -(-1) = 1\).
Since \(1=1\), the bridge is balanced. This means the potential of the two middle nodes are equal. However, the inductor is not in the central arm, it is one of the main arms of the bridge, so its current is not zero. The first interpretation leading to an answer is the most likely intended one.
