Question

The Iceberg Kid, infamous for imposing a deep freeze on whoever disagrees with him, discovers that in his advanced teenaged years his hands constantly feel chilled. As he is a cool physics student, the Iceberg Kid quickly calculates the resistance of the resistor needed to warm his hands. Given that 181 J of thermal energy is generated by the resistor during 9.99 s of operation while connected to a 12.0 V battery, find the correct value of this resistance (and avoid a cold, cold fate).

Answer 1

`7.96 \Omega`

Step-by-step explanation:

First of all, we can calculate the power dissipated by the resistor. We have:

E = 181 J is the energy produced

t = 9.99 s is the time interval

So, the power dissipated is

`P=(E)/(t)=(181 J)/(9.99 s)=18.1 W`

But the power dissipated can also be written as

`P=(V^2)/(R)`

where

V = 12.0 V is the potential difference across the resistor

R is the resistance

Solving for R, we find

`R=(V^2)/(P)=((12.0 V)^2)/(18.1 W)=7.96 \Omega`