NEET Practice Questions (MCQs) with Answers & Solutions

The power dissipated in an AC circuit with a resistor (R) and inductor (L) in series is given by the formula:

$$ P = \frac{V^2 R}{Z^2} $$

where \( Z \) is the impedance of the circuit, which is given by \( Z = \sqrt{R^2 + (\omega L)^2} \). Substituting \( Z^2 \) into the formula, we get:

$$ P = \frac{V^2 R}{R^2 + (\omega L)^2} $$

Thus, the correct option is:

$$ \frac{V^2 R}{(R^2 + \omega^2 L^2)} $$

The resonant frequency (\( f_0 \)) of an LCR circuit is given by the formula:

$$ f_0 = \frac{1}{2\pi \sqrt{LC}} $$

To keep the resonant frequency unchanged when the capacitance is changed from \( C \) to \( 2C \), the inductance \( L \) must be adjusted such that the product \( LC \) remains constant. If \( C \) becomes \( 2C \), then \( L \) must become \( L/2 \) to maintain the same resonant frequency. Therefore, the correct option is:

$$ \frac{L}{2} $$

In an LCR series AC circuit, the voltages across the inductor (L) and capacitor (C) are 180 degrees out of phase. When the circuit is at resonance, the inductive reactance (XL) equals the capacitive reactance (XC), and their voltages cancel each other out. Therefore, the voltage across the LC combination is zero.

In an LCR circuit where the current leads the voltage by $45^ ext{°}$, the circuit is in resonance condition where the net reactance is zero. The capacitive reactance is equal to the inductive reactance ($X_C = X_L$). The condition $ an(45^ ext{°}) = 1$ gives $X_L - X_C = R$. Solving this using the given frequency, the value of capacitance can be found as $C = rac{1}{2 ext{π}f(2 ext{π}fL + R)}$.

$ \upsilon _L = \upsilon_C = I_{X_C} ={\upsilon \over R\omega C} $

When a metallic solid sphere is placed in a uniform electric field, the lines of electric force are distorted due to the conducting nature of the sphere. The field inside the sphere is zero, and the field lines are perpendicular to the surface of the sphere. The correct representation of this phenomenon is shown in option 4, where the lines of force bend around the sphere and are perpendicular at the points where they touch the sphere.

When a plane electromagnetic wave is incident on a material surface, it delivers both momentum and energy. The energy carried by the wave is related to the intensity of the wave, and the momentum is related to the energy by the equation $P = rac{E}{c}$, where $c$ is the speed of light. Therefore, both momentum and energy are non-zero. Hence, the correct option is $P eq 0, E eq 0$.

The velocity of electromagnetic waves in a vacuum is the speed of light, which is approximately $3 imes 10^8$ meters per second. This speed is the same for all types of electromagnetic waves, including gamma rays ($V_ ext{γ}$), X-rays ($V_ ext{x}$), and microwaves ($V_ ext{m}$). Therefore, $V_ ext{γ} = V_ ext{x} = V_ ext{m}$.

According to Maxwell's equations, a changing electric field produces a magnetic field. This relationship is described by the Maxwell-Ampère law: $$ abla imes extbf{E} = -rac{ ext{d} extbf{B}}{ ext{d}t}$$ which indicates that a time-varying electric field generates a magnetic field.