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In the circuit shown below, a three-phase star-connected unbalanced load is connect to a balanced three-phase supply of $100\:\sqrt{3}\:V$ with phase sequence $\text{ABC}$. The star connected load has $Z_{A} = 10\:\Omega$ and $Z_{B} = 20\angle 60^{\circ}\:\Omega$. The value of $Z_{C}$ in $\Omega$, for which the voltage difference across the nodes $n$ and ${n}'$ is zero, is

  1. $20\angle -30^{\circ}$
  2. $20\angle 30^{\circ}$
  3. $20\angle -60^{\circ}$
  4. $20\angle 60^{\circ}$
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