To determine the current flowing in the given a.c. circuit, we need to analyze the components involved: a resistor, an inductor, and a capacitor, all connected in series. The circuit has an electromotive force (e.m.f) of 12V, a resistance of 8Ω, an inductive reactance of 16Ω, and a capacitive reactance of 10Ω. ### Step-by-Step Explanation 1. **Understanding the Components**: - **Resistor (R)**: This component opposes the flow of current and is measured in ohms (Ω). Here, R = 8Ω. - **Inductor (XL)**: This component has inductive reactance, which also opposes the flow of current due to the magnetic field created when current passes through it. Here, XL = 16Ω. - **Capacitor (XC)**: This component has capacitive reactance, which opposes the flow of current due to the electric field created when voltage is applied. Here, XC = 10Ω. 2. **Calculating the Total Reactance**: - In a series circuit, the total reactance (X) is calculated by subtracting the capacitive reactance from the inductive reactance: \[ X = XL - XC = 16Ω - 10Ω = 6Ω \] - This means the circuit has a net reactance of 6Ω. 3. **Calculating the Total Impedance (Z)**: - The total impedance (Z) in a series circuit is given by the formula: \[ Z = \sqrt{R^2 + X^2} \] - Substituting the values we have: \[ Z = \sqrt{(8Ω)^2 + (6Ω)^2} = \sqrt{64 + 36} = \sqrt{100} = 10Ω \] 4. **Calculating the Current (I)**: - Using Ohm's Law, the current (I) in the circuit can be calculated using the formula: \[ I = \frac{V}{Z} \] - Here, V is the e.m.f of the circuit, which is 12V. Thus: \[ I = \frac{12V}{10Ω} = 1.2A \] ### Conclusion The current flowing in the circuit is **1.2A**, which corresponds to option **B**. ### Explanation of Other Options - **Option A (1.4A)**: This value is incorrect because it does not take into account the correct total impedance calculated from the resistance and net reactance. - **Option C (12.0A)**: This value would imply that the impedance is very low, which is not the case here. The calculated impedance is 10Ω, leading to a much lower current. - **Option D (14.0A)**: Similar to option C, this value suggests an unrealistic scenario where the impedance is extremely low, which contradicts the values given for resistance and reactance. ### Common Pitfalls - **Ignoring Reactance**: A common mistake is to overlook the effects of inductive and capacitive reactance when calculating total impedance. - **Misapplying Ohm's Law**: Ensure that the correct values for voltage and impedance are used in Ohm's Law to find current. ### Revision Summary - The total reactance in a series a.c. circuit is the difference between inductive and capacitive reactance. - Total impedance combines resistance and reactance using the Pythagorean theorem. - Current can be calculated using Ohm's Law: \( I = \frac{V}{Z} \). - The correct answer for the current in this circuit is **1.2A (Option B)**.