Question

A 20 volts ac is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is $12 \mathrm{~V}$, the voltage across the coil is, (a) 16 volts (b) 10 volts (c) 8 volts (d) 6 volts

Short answer

The voltage across the coil is 8 volts, which corresponds to option (c).

Step-by-step solution

Apply Kirchhoff's Voltage Law (KVL)

KVL states that the sum of the voltages around a closed loop in a circuit is zero. In this case, we have a simple series circuit with an AC voltage source, a resistor, and a coil. The sum of the voltages across the resistor (\(V_R\)) and the coil (\(V_C\)) must equal the voltage supplied by the AC source (\(V_S\)): \(V_S = V_R + V_C\) We are given \(V_S = 20V\) and \(V_R = 12V\). We can plug these values into the equation to solve for \(V_C\).

Solve for the Voltage Across the Coil (\(V_C\))

Using the equation from Step 1, we can now solve for the voltage across the coil: \(20V = 12V + V_C\) Subtracting 12V from both sides of the equation, we get: \(V_C = 20V - 12V = 8V\) So, the voltage across the coil is 8 volts.

Check for the Correct Answer

We can now look at the given options to see which one matches our calculated voltage across the coil: (a) 16 volts (b) 10 volts (c) 8 volts (d) 6 volts The correct answer is (c) 8 volts.