The Resistance of a Heater Coil is 110 Ohm

By Aina Parasher|Updated : July 6th, 2022

The resistance of a heater coil is 110 Ω. A resistance R is connected in parallel with it and combination is joined in series with a resistance of 11 Ω to a 220 V main line. The heater operates with a power of 110 W. The value of R in ohm is-

  1. 12.22 
  2. 24.42
  3. 14.24
  4. That the given is not correct

Answer: A. 12.22

The Resistance of a Heater Coil is 110 Ohm, the value of resistance R in Ohm is 12.22.

Solution:

Resistance of hear coil Rheater=110 ohm

And power through heater coil Pheater= 110 W= (voltage across heater coil)2/resistance of heater coil=(Vheater)2/Rheater

(Vheater)= 110×110

so, voltage across inductor Vheater=110 Volts

then current through the heater Iheater=voltage across heater/resistance of heater

Iheater=110 V/110 Ω =1 Amp

As heater and resistor R are connected in parallel voltage across them will be same,

So, voltage across resistor VR= 110 Volts

Then voltage across the 11-ohm resistor I11Ω =voltage across 11 Ω resistor/ resistance

I11Ω =110/11=10 amps

Hence current through resistor R is IR= I11Ω - Iheater

IR=10-1

IR=9 amps

The resistance R=voltage across resistor R/current through resistor R

 R=V11Ω/I11Ω =110 V/9 A=12.22 Ω.

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