When 100 volt d.c is applied across a solenoid a current of 1.0 A flows in it. When 100 volt a.c. is

Question

When 100 volt d.c is applied across a solenoid a current of 1.0 A flows in it. When 100 volt a.c. is applied across the same coil, the current drops to 0.5 A . If the frequency of the a.c source is 50 Hz the impedance and inductance of the solenoid are\

Professor PC Thomas Classes · Answer

For d.c. $X_{L}=0$\ $	herefore \mathrm{R}=\frac{\mathrm{V}_{\mathrm{dc}}}{\mathrm{I}_{\mathrm{dc}}}=\frac{100}{1}=100 \Omega$\ For a.c.\ $\mathrm{Z}=\frac{\mathrm{V}_{\mathrm{acx}}}{\mathrm{I}_{\mathrm{ac}}}=\frac{100}{0.5}=200 \Omega$\ $	herefore \mathrm{X}_{\mathrm{L}}=\sqrt{\mathrm{Z}^{2}-\mathrm{R}^{2}}=\sqrt{200^{2}-100^{2}}$\ $=100 \cdot \sqrt{3} \Omega 	herefore \mathrm{~L}=\frac{\mathrm{X}_{\mathrm{L}}}{2 \pi \mathrm{f}}=$\