resistance of a bulb filament is 100 ohm at a temperature of 100° Celsius .If the temperature coefficient of resistance 0.005 per °C ,its resistance will become 200 ohm at a temperature of:
Hello Aspirant,
We have
Initial resistance =100 ohm
Final resistance = 500 ohm
Temperature coefficient, α=0.005Ω/ °C
Final temperature = 100 °C
If we formulate the above values in the equation
200 = 100[ 1+ 0.005( Final temperature - 100)]
=> Final temperatures = 300 ° C
Hey aspirant,
For your given query, i will give you the concept from which your problem will be solved.
Here , it is :
See, the resistance of the conductor changes when the temperature of that conductor changes.
then , new resistance is given by :
R(t) = R(0) [ 1 + alpha T ]
now , let resistance of bulb filament be R(0) at 0°C
Resistance of the bulb filament at 100°C(R) = 100ohm
The change in temperature in the first case will be
T = (100°-0°)C = 100°C
Then, resistance is given by above formula , put the values in the above formula then we get :
100 = R(0) [ 1+0.005×100 ]
100 = 1.5 R (0) _________ (a)
The temperature of the bulb filament at R = 200 ohm is T'
Hence, the resistance of the bulb's filament is given by ,
R' = R ( 1+alpha T )
200 = R(o) [ 1+0.005×T' ] ________(b)
Now , divide equation a and b then we get ,
T' = 400°C
I hope this will be helpful for you.
Revert back if i miss something.
Good luck !!!!
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