Question

Question 3.8: Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10 −4 °C −1 .

Class 12 - Physics - Current Electricity Current Electricity Page-127

Answer 1

at room temperature 27°C , the resistance of the heating element is $R_{27^{\circ}}= \frac{230}{3.2}=71.875\Omega$
[ according to Ohm's law, V = IR , so , R = V/I ]

at the steady temperature t°C , the resistance ,
$R_t$=230/2.8 = $82.143\Omega$

now, use the relation, $R=R_0[1+\alpha(T-T_0)]$
here, R=R_t = 82.143$\Omega$
$R_0=R_{27^{\circ}}=71.875\Omega$
$\alpha=1.7\times10^{-4}/^{\circ}C$

now, 82.143 = 71.875 [1 + 1.7 × 10^-4(t - 27)]
=> 82.143 - 71.875 = 71.875 × 1.7 × 10^-4(t - 27)
=> 0.084 × 10^4 = t - 27
=> 840 + 27 = t
=> t = 867°C

hence, temperature = 867°C

Answer 2

Answer:867°C

Explanation:

at room temperature 27°C , the resistance of the heating element is

[ according to Ohm's law, V = IR , so , R = V/I ]

at the steady temperature t°C , the resistance ,

=230/2.8 =

now, use the relation,

here, R=R_t = 82.143

now, 82.143 = 71.875 [1 + 1.7 × 10^-4(t - 27)]

=> 82.143 - 71.875 = 71.875 × 1.7 × 10^-4(t - 27)

=> 0.084 × 10^4 = t - 27

=> 840 + 27 = t

=> t = 867°C

hence, temperature = 867°C