An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature (27.0° C ) is found to be 75.3 Ω. When the toaster is connected to a 230 V supply, the current settles, after a few seconds to a steady value of 2.68 A. The temperature coefficient of resistance is 1.7 × 10-4 ° C -1 . The steady temperature of the nichrome element is

Question

An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature (27.0° C ) is found to be 75.3 Ω. When the toaster is connected to a 230 V supply, the current settles, after a few seconds to a steady value of 2.68 A. The temperature coefficient of resistance is 1.7 × 10-4 ° C -1 . The steady temperature of the nichrome element is (A) 747° C (B) 847° C (C) 897° C (D) 927° C

Tardigrade Admin · Accepted Answer

R2=(230 V /2.68 A )=85.8 Ω Using, R2=R1[(1+α(T2-T1)]. 85.8=75.3(1+(1.7 × 10-4)(T2-27° C )) ⇒ T2=((85.8-75.3)/(75.3 × 1.7 × 10-4))+27 =820+27=847° C .

$74 7^{\circ} C$

$84 7^{\circ} C$

$89 7^{\circ} C$

$92 7^{\circ} C$

$R_{2} = \frac{230 V}{2.68 A} = 85.8Ω$
Using, $R_{2} = R_{1} [(1 + α (T_{2} - T_{1})]$
$85.8 = 75.3 (1 + (1.7 \times 1 0^{- 4}) (T_{2} - 2 7^{\circ} C))$
$\Rightarrow T_{2} = \frac{( 85.8 - 75.3 )}{( 75.3 \times 1.7 \times 1 0 ^{- 4} )} + 27$
$= 820 + 27 = 84 7^{\circ} C .$

747∘C

847∘C

897∘C

927∘C

R2​=2.68A230V​=85.8Ω Using, R2​=R1​[(1+α(T2​−T1​)] 85.8=75.3(1+(1.7×10−4)(T2​−27∘C)) ⇒T2​=(75.3×1.7×10−4)(85.8−75.3)​+27 =820+27=847∘C.

$74 7^{\circ} C$

$84 7^{\circ} C$

$89 7^{\circ} C$

$92 7^{\circ} C$

$R_{2} = \frac{230 V}{2.68 A} = 85.8Ω$
Using, $R_{2} = R_{1} [(1 + α (T_{2} - T_{1})]$
$85.8 = 75.3 (1 + (1.7 \times 1 0^{- 4}) (T_{2} - 2 7^{\circ} C))$
$\Rightarrow T_{2} = \frac{( 85.8 - 75.3 )}{( 75.3 \times 1.7 \times 1 0 ^{- 4} )} + 27$
$= 820 + 27 = 84 7^{\circ} C .$