A 20   V AC is applied to a circuit consisting of a resistor and a coil with negligible resistance. If…

As the resistance and coil or inductor are in series with power supply, therefore the voltage in the inductor will lead the voltage in resistor by $90°,$the phasor diagram is, 

So, $V_{\mathrm{net}}=20 \mathrm{V}=\sqrt{V_{\mathrm{R}}^2+V_{\mathrm{I}}^2}$and given that $V_{\mathrm{R}}=12 \mathrm{V}$

Therefore, $V_{\mathrm{I}}=\sqrt{{20}^2-{12}^2}=16 \mathrm{V}$

Hence, voltage across the coil is, $16 \mathrm{V}$