But the answer is 200j

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Answer

200j A200j\,\mathrm{A}

Step-by-step solution

3 steps
  1. Write the formula for current in a circuit.

    I=VZI = \frac{V}{Z}
  2. Identify the values with units.

    Voltage V=100 VV = 100\,\mathrm{V}, capacitive impedance Z=−j 0.5 ΩZ = -j\,0.5\,\Omega.
    Substitute into the formula:

    I=100 V−j 0.5 ΩI = \frac{100\,\mathrm{V}}{-j\,0.5\,\Omega}
  3. Simplify the denominator.

    Multiply numerator and denominator by the conjugate of the denominator or rewrite:

    1−j=1−j⋅jj=j(−j)j=j−j2=j1=j\frac{1}{-j} = \frac{1}{-j} \cdot \frac{j}{j} = \frac{j}{(-j)j} = \frac{j}{-j^2} = \frac{j}{1} = j

    So,

    I=100 V0.5 Ω⋅j=200 A⋅jI = \frac{100\,\mathrm{V}}{0.5\,\Omega} \cdot j = 200\,\mathrm{A} \cdot j

    Final answer: 200j A\boxed{200j\,\mathrm{A}}

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