Question

The current through a certain heater wire is found to be fairly independent of its temperature. If the current through the heater wire is doubled, the amount of energy delivered by the heater in a given time interval will:_______.a) increase by a factor of two. b) decrease by a factor of two. c) increase by a factor of four.d) decrease by a factor of four. e) increase by a factor of eight.

Answer 1

Answer:

(c) increase by a factor of four

Explanation:

the formular for the relationship between  energy and current is E= I²Rt (Heat energy)

the heater is fairly independent of its temperature , and given the time to be constant.

with the current being doubled,

E = I² Rt

E/ I² = K

$\frac{E1}{I1^{2} }$ =$\frac{E2}{I2^{2} }$

E2 = $\frac{E1* I1^{2} }{I1^{2} }$

I2 = 2* I1

E2 =  E1 * 4*I1² / I1²

dividing , we have that  E2 = 4 * E1

which means during the same time interval the amount of energy will increase by a factor of four.