Question

(a) If a copper heating element is connected to a source of constant voltage, does the electrical power consumed by heating element increase or decrease as its temperature increase? Explain. (b) A resistor in the form of Carbon cylinder is connected to the voltage source. As the temperature of the cylinder increase, does the electrical power it consumes increase or decrease? Explain.

Short answer

(a) The electrical power consumed by heating element decrease as its temperature increase.

(b) The electrical power it consumes increase as the temperature of the cylinder increase.

Step-by-step solution

Definition of resistor

The term resistor may be defined a device which do not flow the electric current freely through the circuit.

Determine the effect of temperature on copper heating element and Carbon cylinder.

(a) With constant voltage and the power is$\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$ which state that power is inversely proportional to the resistance and temperature coefficient of the copper is positive. It means more the resistance as more the temperature. The equation which also hold this statement

${\mathrm{R}}_{\mathrm{T}}={\mathrm{R}}_{\mathrm{o}}[1+\mathrm{\alpha }(\mathrm{T}-{\mathrm{T}}_{\mathrm{o}}\left)\right]$

Hence, the electrical power consumed by heating element decrease as its temperature increase.

(b) Temperature coefficient of the carbon is negative. It means less the resistance as more the temperature. The equation which also hold this statement

${\mathrm{R}}_{\mathrm{T}}={\mathrm{R}}_{\mathrm{o}}[1+\mathrm{\alpha }(\mathrm{T}-{\mathrm{T}}_{\mathrm{o}}\left)\right]$

Hence, the electrical power it consumes increase as the temperature of the cylinder increase.