Q. 24

(i) An a.c. sourc

Answer :

(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


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