A resistor has a resistance of 30 $\Omega$ at 20$^{\circ}$C.If the temperature coefficient is 4.5 $\times$10³ $^{\circ}$C^-1,what is its resistance at 200$^{\circ}$C? A) 24 $\Omega$ B) 27 $\Omega$ C) 48 $\Omega$ D) 54 $\Omega$ E) 57 $\Omega$

Question

Quizplus · Accepted Answer

We can use the formula:
R2 = R1(1 + αΔT)
where R1 is the initial resistance at 20°C, α is the temperature coefficient, ΔT is the change in temperature (in °C) and R2 is the resistance at the new temperature.

Substituting the given values:
R1 = 30 Ω
α = 4.5 × 10^-3 / °C
ΔT = (200 - 20)°C = 180°C

R2 = 30 Ω (1 + 4.5 × 10^-3 / °C × 180°C)
R2 = 30 Ω (1 + 0.81)
R2 = 30 Ω × 1.81
R2 = 54.3 Ω
Rounding off to two significant figures, we get:
R2 = 54 Ω

Therefore, the resistance at 200°C is 54 Ω which is option D.

A Resistor Has a Resistance of 30 Ω\OmegaΩ At 20 ∘^{\circ}∘ CIf the Temperature Coefficient Is 4

A Resistor Has a Resistance of 30 $\Omega$ At 20 $^{\circ}$ CIf the Temperature Coefficient Is 4