A transformer is used to charge the alternating voltage to a high or low value. A power transmission line feeds input power of 230 V to a step-down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V ?

Give: The input voltage to the transformer is 230 V The number of turns in primary windings is 4000 turns The output voltage of the transformer is 230 V The number of turns in the secondary coil is given by: V 1 V 2 = n 1 n 2 n i = 4000 , V 2 = 230 and V 1 = 230 n 2 = n 1 × V 2 V 1 n 2 = 4000 × 230 230 = 4000 n 2 = 4000 Hence, it is the required answer.

A transformer is used to charge the alternating voltage to a high or low value. What is the principle of a transformer?

The transformer works on the principle of faraday's law of electromagnetic induction and mutual induction. There are usually two coils primary coil and secondary coil on the transformer core. The core laminations are joined in the form of strips. The two coils have high mutual inductance. When an alternating current pass through the primary coil it creates a varying magnetic flux. As per faraday’s law of electromagnetic induction, this change in magnetic flux induces an emf (electromotive force) in the secondary coil which is linked to the core having a primary coil. This is mutual induction. Hence, it is the required answer.

A series LCR circuit connected to an ac source is shown below: Under what condition this circuit is used for tuning radio?

Resonant circuits are used in tuning of a radio. Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedances or admittances of circuit elements cancel each other. Resonance is the phenomenon in the electrical circuit, where the output of the electrical circuit is maximum at one particular frequency. That particular frequency is known as the resonant frequency.

A series L.C.R circuit connected to an AC Source is shown below: Write an expression for impedance offered by this circuit.

We know that the voltage drop across a resistance is V R = IR . Where, I is the current in the circuit and R is the resistance of the circuit. The voltage across a inductor coil is, V L = IX L Where X L = jωL is the inductive impedance, L is the inductance of the coil, ω is the frequency of the AC source. The voltage drop across a capacitor is V C = IX C . Where, X C = 1 jω C is the capacitive impedance, C is the capacitance of the capacitor. Now, for a series L.C.R circuit, we can observe the voltage drops across each component as by the equations given above. Now, we have to plot the phasor diagram. We can see that the voltage across L is a pure imaginary type quantity, so it will be leading current I by 90 ° (is on the positive Y Axis). The voltage across C is also a pure imaginary type quantity, hence it will lag current by 90 ° S i n c e 1 j = − j , so it will be on the negative Y axis of the phasor diagram. Voltage across R is a real quantity hence it will be in phase with the current I . The net voltage drop across the circuit will be a complex quantity as V NET = V R + V C + V L . So, = IR + IX C + IX L = IR + jI ωL − 1 ωC So, the V NET Will be on the positive complex XY Plane. So, the phasor diagram of the circuit is given in the diagram. Now, we want to find the impedance Z of the circuit. If we use Pythagoras theorem from the diagram (or take modulus on the both sides of the expression of V NET ) we get, V NET 2 = VR 2 + ( VL − VC ) 2 Now, putting the values of V L , V C and V R in the phase or complex plane. ∴ ( IZ ) 2 = ( IR ) 2 + IωL − I ωC 2 Cancelling out I from both sides we get, ⇒ ( Z ) 2 = ( R ) 2 + ωL − 1 ωC 2 Hence, taking square root of the equation we get the expression of impedance as, ⇒ Z = ( R ) 2 + ωL − 1 ωC 2 Hence, it is the required answer.

The phaser diagram of the alternating voltage across an unknown device X and current flowing through it are shown below. Draw the phaser diagram which shows the relation among V R , V L , V C and I In a series L.C.R circuit.

The phaser diagram which shows the relation among V R , V L , V C and I In a series L.C.R circuit. Hence, it is the required answer.

The phaser diagram of the alternating voltage across an unknown device X and current flowing through it are shown below. Draw the graphical variation of current and voltage with ωt through this device.

The graphical variation of current and voltage with ωt through this device. Hence, it is the required answer.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Kerala Board-2020>Q 8

MEDIUM

12th Kerala Board

IMPORTANT

Earn 100

The current through an AC circuit depends on the magnitude of the applied voltage and impedance of the circuit.

Write any two factors on which the impedance of a series LCR circuit depends.

Important Questions on Alternating Current

MEDIUM

12th Kerala Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Kerala Board-2020>Q 9

The current through an AC circuit depends on the magnitude of the applied voltage and impedance of the circuit.

Draw and impedance diagram of a series LCR circuit and write the expression for the power factor from the diagram.

MEDIUM

12th Kerala Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Kerala Board-2020>Q 10

The current through an AC circuit depends on the magnitude of the applied voltage and impedance of the circuit.

A sinusoidal voltage of peak value $283 V$ and frequency $50 Hz$ is applied to a series LCR circuit in which $R = 3 Ω, L = 25.48 mH, and C = 796 μF$ . Find the impedance of the circuit.