Example 105. A nichrome heating element across
230 V supply consumes 1.5 kW of power and heats up to a
temperature of 750°C. A tungsten bulb across the same supply
operates at a much higher temperature of 1600°C in order to
be able to emit light. Does it mean that the tungsten bulb
necessarily consumes greater power ?-(b) Which of the two
has greater resistance : a1 kW heater or a 100 W tungsten
bulb, both marked for 230 V ?
[NCERT
Answers
Answer:
Answer :
A::D
Solution :
E=220V
P=60W
,R = (V^2)/(P) = 220xx(220)/(60) = 806.67 Omega (a) E' = 180V P' = (V^2)/(R ) = 40.16 =40 W (b) E'' =240VP''= (V^2)/(R )=71.4 W= 71W`.
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Answer:
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Explanation:
at room temperature 27°C , the resistance of the heating element is R_{27^{\circ}}= \frac{230}{3.2}=71.875\OmegaR
27
∘
=
3.2
230
=71.875Ω
[ according to Ohm's law, V = IR , so , R = V/I ]
at the steady temperature t°C , the resistance ,
R_tR
t
=230/2.8 = 82.143\Omega82.143Ω
now, use the relation, R=R_0[1+\alpha(T-T_0)]R=R
0
[1+α(T−T
0
)]
here, R=R_t = 82.143\OmegaΩ
R_0=R_{27^{\circ}}=71.875\OmegaR
0
=R
27
∘
=71.875Ω
\alpha=1.7\times10^{-4}/^{\circ}Cα=1.7×10
−4
/
∘
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