Physics MCQs for NEET — Practice Questions with Answers

The power dissipated in an AC circuit depends on the phase difference between voltage (V) and current (I). When V and I are in phase, the power is maximized, and when they are out of phase, the power is reduced. This relationship is given by the formula: \( P = VI \cos(\phi) \), where \( \phi \) is the phase angle between V and I.

When the voltage is stepped up n times in the transmission of AC power, the current decreases by n times. Since power loss in transmission lines is proportional to the square of the current (\( P_{loss} = I^2 R \)), the power loss decreases by \( n^2 \) times. Therefore, stepping up the voltage n times decreases the power loss by \( n^2 \) times.

The average value of a sinusoidal voltage over one complete cycle is zero. This is because the positive half-cycle cancels out the negative half-cycle. Mathematically, the integral of a sine function over one complete cycle (from 0 to 2Ï€) is zero.

The AC voltage can be represented as $V(t) = V_0 ext{sin}( heta)$ where $V_0$ is the peak voltage. For a frequency $f = 50 ext{ Hz}$, the angular frequency $ heta = 2 ext{Ï€}f = 100 ext{Ï€} ext{ rad/s}$. The voltage changes from its peak value to zero in a quarter cycle, which is $T/4$ where $T = 1/f$. Therefore, $T = 1/50 = 0.02 ext{ s}$ and $T/4 = 0.02/4 = 0.005 ext{ s} = 5 imes 10^{-3} ext{ s}.$

The given voltage is $ ext{ε} = 80 ext{ sin } 100 ext{π} t $ and the impedance is $ 20 ext{ Ω}$. The peak value of voltage $V_0 = 80$ V. The effective (RMS) value of voltage is $V_{ ext{rms}} = V_0/ ext{√2} = 80/ ext{√2} = 56.57$ V. Using Ohm's law, the effective current $I_{ ext{rms}} = V_{ ext{rms}}/Z = 56.57/20 = 2.828$ A.

A choke coil is designed to have high inductance and low resistance. The high inductance allows it to effectively block high-frequency AC signals, while the low resistance minimizes power loss in the form of heat.

with help pf phasor $ \upsilon = \sqrt {\upsilon _R^2 + \upsilon _C^2 } $

The average power in an AC circuit is given by the formula: \[ P_{avg} = \frac{E_0 I_0}{2} \cos \varphi \] where \( E_0 \) is the peak emf, \( I_0 \) is the peak current, and \( \varphi \) is the phase difference between the emf and the current. This formula is derived from the general power formula for AC circuits and accounts for the phase difference.

The impedance \( Z \) of a series circuit containing resistance \( R \) and inductance \( L \) is given by: \[ Z = \sqrt{R^2 + (\omega L)^2} \] where \( \omega = 2\pi f \) is the angular frequency. Substituting \( \omega \), the impedance becomes: \[ Z = \sqrt{R^2 + (2\pi fL)^2} \]

$ I = { \epsilon _0 \over \sqrt { R^2 + \omega^2 L^2 } } = { \epsilon _0 \over R \sqrt {1 + ({ \omega L \over R }) ^2 }} = { I _0 \over \sqrt {1 + ({ \omega L \over R }) ^2 }}$