Alternating Current

A step up transformer operates on a 230 V line and a load current of 2 ampere. The ratio of the primary and secondary winding is 1 : 25. What is the current in the primary ?

by

Q: A step up transformer operates on a 230 V line and a load current of 2 ampere. The ratio of the primary and secondary winding is 1 : 25. What is the current in the primary ?

Sol: using the relation ,

$\large \frac{N_s}{N_p} = \frac{I_s}{I_p} $

$\large I_s = \frac{N_s}{N_p} \times I_p $

$\large I_s = \frac{25}{1} \times 2 $

= 50 A

A transformer having efficiency 90% is working on 100 V and at 2.0 kW power. If the current in the secondary coil is 5A, calculate the current in the primary coil…

by

Q: A transformer having efficiency 90% is working on 100 V and at 2.0 kW power. If the current in the secondary coil is 5 A, calculate (i) the current in the primary coil and (ii) voltage across the secondary coil.

Sol: Here , η = 90% = 9/10, Is = 5 A , Ep = 100 V,

(i) Ep Ip = 2 kW = 2000 W

Ip = 2000/Ep or Ip = 2000/100 = 20 A

(ii) $\large \eta = \frac{Output \; Power}{Input \; Power}$

$\large \eta = \frac{E_s I_s}{E_p I_p}$

Es Is = η × Ep Ip

Es Is = (9/10) × 2000 = 1800 W

Es = 1800 /Is = 1800/5

Es = 360 volt

An electric bulb has a rated power of 50 W at 100 V. If it used on an AC source of 200 V, 50 Hz, a choke has to be used in series with it. This choke should have an inductance of

by

Q: An electric bulb has a rated power of 50 W at 100 V. If it used on an AC source of 200 V, 50 Hz, a choke has to be used in series with it. This choke should have an inductance of

Sol: Here, P = 50 W, V = 100 Volt

I = P/V = 50/100 = 0.5 A, R = V/I = 100/0.5 = 200 Ω

Let L be the inductance of the choke coil .

$\large I_v = \frac{E_v}{Z} $

$\large Z = \frac{E_v}{I_v} = \frac{200}{0.5} $

Z = 400 Ω

Now , $\large X_L = \sqrt{Z^2 – R^2}$

$\large X_L = \sqrt{400^2 – 200^2} = 200\sqrt{3} $

$\large \omega L = 200\sqrt{3} $

$\large L = \frac{200\sqrt{3}}{\omega} = \frac{200\sqrt{3}}{2 \pi f} $

$\large L = \frac{200\sqrt{3}}{100 \pi} $

L = 1.1 H

An ideal choke coil takes a current of 8 ampere when connected to an AC supply of 100 volt and 50 Hz. A pure resistor under the same condition takes a current of 10 ampere….

by

Q: An ideal choke coil takes a current of 8 ampere when connected to an AC supply of 100 volt and 50 Hz. A pure resistor under the same condition takes a current of 10 ampere. If the two are connected to an AC supply of 150 volts and 40 Hz. Then the current in a series combination of the above resistor and inductor is

Sol: For pure inductor,

$\large X_L = \frac{100}{8} = \frac{25}{2} ohm$

$\large \omega L = \frac{25}{2} ohm$

$\large L = \frac{25}{2 \omega } = \frac{25}{2 \times 2 \pi \times 50} $

= 1/8π H

$\large R = \frac{V}{I}= \frac{100}{10} $

= 10 ohm

For the combination, the supply is 150 v, 40 Hz

∴ XL = ω L = 2π × 40 × (1/8π ) = 10 ohm

$\large Z = \sqrt{R^2 + X_L^2 }$

$\large Z = \sqrt{10^2 + 10^2 } $

= 10√2 ohm

$\large I_v = \frac{E_v}{Z} = \frac{150}{10\sqrt{2}} = \frac{15}{\sqrt{2}} A$