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

Answer:

$7.96 \Omega$

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

$P=\frac{E}{t}=\frac{181 J}{9.99 s}=18.1 W$

But the power dissipated can also be written as

$P=\frac{V^2}{R}$

where

V = 12.0 V is the potential difference across the resistor

R is the resistance

Solving for R, we find

$R=\frac{V^2}{P}=\frac{(12.0 V)^2}{18.1 W}=7.96 \Omega$