Q.30. Read the following paragraph and answer the questions that follow. A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors capacitors can be arranged in series or parallel or a combination of both to obtain desired value of capacitance. (i) Find the equivalent capacitance between points A and B in the given diagram. (ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The electric field between the plates decreases. Explain. (iii) A capacitor A of capacitance C having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A. Or (iii) Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation as shown in figure. Find an expression for capacitance of the system. Q.31 An interesting characteristic of the series LCR circuit is the phenomenon of resonance. The phenomenon of resonance is common among systems that have a tendency to oscillate at a particular frequency. This frequency is called the system's natural frequency. If such a system is driven by an energy source of a frequency that is near the natural frequency, the amplitude of the oscillation is found to be large. Resonant circuits have a variety of applications, for example, in the tuning mechanism of a radio or a TV set. The antenna of a radio accepts signal from many broadcasting stations. The signals picked up in the antenna acts as a source in the tuning circuit of the radio, so the circuit can be driven at many frequencies. But to hear one particular radio station, we tune the radio, so that resonant frequency of the circuit becomes nearly equal to the frequency of radio signal received.  Now, answer the following questions:- (1) If the value of 'C' is decreased in a series LCR circuit, then resonant frequency (a) increases. (b) decreases. (c) is not affected. (d) is reduced to zero. (ii) Power factor is one for (a) pure inductor (b) pure capacitor (c) pure resistor (d) either an inductor or a capacitor (iii) As X_{L} = X_{C} in a series LCR circuit, the impedance (a) purely resistive (b) purely inductive (c) purely capacitive (d) capacitive or inductive (iv) Power factor of an inductive series LCR circuit can be improved by using (a) a capacitor in series. (b) a capacitor in parallel with the capacitor of LCR circuit. (c) a capacitor in parallel with the series LCR circuit. (d) an inductor in series with the series LCR circuit. Or (iv) Current in the circuit is wattless if (a) inductance in the circ