The current lags the applied voltage in the circuit shown. 10 amps Select one: O True O False Check R=60 X = 102
The correct answer and explanation is:
Correct Answer: ✔ True
Explanation (Approx. 300 Words)
In AC (Alternating Current) circuits, the relationship between the current and the voltage depends on the type of components present—resistors (R), inductors (L), and capacitors (C).
In the circuit mentioned, you have:
- Resistance (R) = 60 ohms
- Reactance (X) = 102 ohms
The total impedance ZZ of the circuit is given by: Z=R2+X2=602+1022=3600+10404=14004≈118.3 ΩZ = \sqrt{R^2 + X^2} = \sqrt{60^2 + 102^2} = \sqrt{3600 + 10404} = \sqrt{14004} \approx 118.3 \, \Omega
The presence of reactance (X) implies that either an inductor or a capacitor is in the circuit. Since the current is said to lag the voltage, X = 102 ohms must be inductive reactance (denoted XLX_L) because:
- In pure resistive circuits, voltage and current are in phase.
- In inductive circuits, current lags voltage.
- In capacitive circuits, current leads voltage.
So, since current lags the applied voltage, this lag must be due to the inductive reactance, which is typical behavior in an RL circuit (Resistor + Inductor).
This lag can also be understood using the phase angle θ\theta between the voltage and current: tan(θ)=XLR=10260=1.7⇒θ≈60.3∘\tan(\theta) = \frac{X_L}{R} = \frac{102}{60} = 1.7 \Rightarrow \theta \approx 60.3^\circ
A positive phase angle means that the current lags behind the voltage by about 60 degrees, confirming inductive behavior.
Since the circuit is inductive in nature due to the presence of XLX_L, and current lags voltage in such a case, the statement is True.
Answer: ✅ True – The current lags the applied voltage in the given circuit.