The Resistance of a Heater Coil is 110 Ohm

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 R_heater=110 ohm

And power through heater coil P_heater= 110 W= (voltage across heater coil)²/resistance of heater coil=(V_heater)²/R_heater

(V_heater)² = 110×110

so, voltage across inductor V_heater=110 Volts

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

I_heater=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 V_R= 110 Volts

Then voltage across the 11-ohm resistor I_11Ω =voltage across 11 Ω resistor/ resistance

I_11Ω =110/11=10 amps

Hence current through resistor R is I_R= I_11Ω – I_heater

I_R=10-1

I_R=9 amps

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

 R=V_11Ω/I_11Ω =110 V/9 A=12.22 Ω.

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