Alternating Current MCQs for NEET — Physics Questions with Answers

The 'Points to Ponder' section clarifies: 'Though in a phasor diagram, voltage and current are represented by vectors, these quantities are not really vectors themselves. They are scalar quantities. It so happens that the amplitudes and phases of harmonically varying scalars combine mathematically in the same way as do the projections of rotating vectors... The ‘rotating vectors’ that represent harmonically varying scalar quantities are introduced only to provide us with a simple way of adding these quantities using a rule that we already know as the law of vector addition.'

According to the NCERT text, 'Though voltage and current in ac circuit are represented by phasors – rotating vectors, they are not vectors themselves. They are scalar quantities.' The representation by phasors is a mathematical convenience to add these quantities using vector addition rules for their amplitudes and phases.

The NCERT text states, 'From Fig. 7.4(a) we see that phasors V and I for the case of a resistor are in the same direction. This is so for all times. This means that the phase angle between the voltage and the current is zero.'

While not explicitly stated in the provided snippets for a purely inductive circuit, the text mentions for an RLC circuit that 'VL is $\pi/2$ ahead of I'. This implies that in a purely inductive circuit, the voltage across the inductor leads the current by $\pi/2$ or 90 degrees.

The NCERT text states, 'The current through the capacitor is $\pi/2$ ahead of the applied voltage.'

According to the NCERT text, 'From previous section, we know that VR is parallel to I, VC is $\pi/2$ behind I and VL is $\pi/2$ ahead of I.'

The NCERT text states, 'The phasor relation whose vertical component gives the above equation is $\text{VL} + \text{VR} + \text{VC} = \text{V}$'.

The NCERT text explains, 'If XC > XL, $\phi$ is positive and the circuit is predominantly capacitive. Consequently, the current in the circuit leads the source voltage.'

From the impedance diagram (Fig. 7.12) and the formula for impedance $Z = \sqrt{R^2 + (X_C - X_L)^2}$, the vertical side of the right-triangle is $(X_C - X_L)$ or $(X_L - X_C)$ depending on which reactance is larger. The magnitude is $|X_C - X_L|$.

The NCERT text states, 'This method of analysing ac circuits suffers from certain disadvantages. First, the phasor diagram say nothing about the initial condition.'