Q24 of 26 Page 1

(i) An a.c. source of voltage V = V0 sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2.


OR


(i) Write the function of a transformer. State its principle of working with the help of a diagram. Mention various energy losses in this device.


(ii) The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W. Calculate


(a) Number of turns in secondary


(b) Current in primary


(c) Voltage across secondary


(d) Current in secondary


(e) power in secondary


(i) The voltage the source is given as




Now the current flowing in the circuit is


The peak voltage across Resistance is



The peak voltage across Inductor is



The peak voltage is ahead of


The peak voltage across Capacitor is



The peak voltage is behind by


The reactive voltage is represented by the difference of



Therefore, the voltage difference) represented in terms of we get



Now the impedance of the circuit is





Now if the value of, the current and the voltage are in same phase.


Therefore, in such condition the circuit is called non-inductive circuit.


(ii) The ratio of the power factor


Given


In a series LR circuit XL = R and power factor of the circuit is P1. XL = XC is put in series to capacitance as C, the power factor is P2.


Formula Used


The ratio between the resistance and the impedance formed in the circuit.



where


P is the power factor, Z is the impedance, R is the resistance.


When LR circuit XL = R and power factor of the circuit is P1


The value of the power factor




When XL = XC is put in series to capacitance as C, the power factor is P2.


The value of the power factor



Therefore, the ratio of the power factors is



OR


A transformer is a device which is used to change low alternating voltage to a high alternating voltage and again from high to low voltage. The working of transformer is done on mutual induction meaning a soft core iron is used which produces an alternating magnetic field which in turn produces alternating current on another coil.



The above diagram represents the working of a transformer, now as for the energy losses we have:


1. Flux leakage due to air induction in the coils and poor structure.


2. Loss of energy due to Eddy Current in case of lack or poor lamination of the coils.


3. Heating losses in resistance due to poor windings.


(ii) (a)


The number of secondary turns is


Given


The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W.


Formula Used


The transformer ratio is equal to the ratio of the secondary winding number to the primary winding number which his given by



where


is the number of secondary winding and is the number of primary winding, n is the transformer ratio.


Therefore, the number of secondary turns is




(b) The current in the primary coil is


Given


The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W.


Formula Used


The power generated by the transformer is the product of current and voltage in the primary turning



where


is the primary current, is the primary voltage, P is the power


The current generated in the primary core is




(c) the voltage in secondary coil is


Given


The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W.


Formula Used


The transformer ratio is equal to the ratio of the secondary winding voltage to the primary winding voltage which his given by



where


is the voltage of secondary winding and is the voltage of primary winding, n is the transformer ratio.


Therefore, the voltage in secondary coil is




(d) The current in the secondary coil is


Given


The secondary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 22000 V and 1100 W.


Formula Used


The power generated by the transformer is the product of current and voltage in the secondary turning



where


is the secondary current, is the secondary voltage, P is the power


The current generated in the secondary core is




(e) In case of ideal transformer the power in the secondary coil = power in the primary coil = 1100 W


More from this chapter

All 26 →
22

Draw a schematic ray diagram of reflecting telescope showing how rays coming from a distant object are received at the eye-piece. Write its two important advantages over a refracting telescope.

 23

Meeta’s father was driving her to the school. At the traffic signal she noticed that each traffic light was made of many tiny lights instead of a single bulb. When Meeta asked this question to her father, he explained the reason for this.

Answer the following questions based on above information:


(i) What were the values displayed by Meeta and her father?


(ii) What answer did Meeta’s father give?


(iii) What are the tiny lights in traffic signals called and how do these operate?


 25

(i) In Young’s double slit experiment, deduce the condition for (a) constructive, and (b) destructive interference at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position ‘x’ on the screen.

(ii) Compare the interference pattern observed in Young’s double slit experiment with single slit diffraction pattern, pointing out three distinguishing features.


OR


(i) Plot a graph to show variation of the angle of deviation as a function of angle of incidence for light passing through a prism. Derive an expression for refractive index of the prism in terms of angle of minimum deviation and angle of prism.


(ii) What is dispersion of light? What is its cause?


(iii) A ray of light incident normally on one face of a right isosceles prism is totally reflected as shown in fig. What must be the minimum value of refractive index of glass? Give relevant calculations.



 26

(i) Define the term drift velocity.

(ii) On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?


(iii) Why alloys like constantan and manganin are used for making standard resistors?


OR


(i) State the principle of working of a potentiometer.


(ii) In the following potentiometer circuit AB is a uniform wire of length 1 m and resistance 10 Ω. Calculate the potential gradient along the wire and balance length AO ( = l).