Question

When a current of 4.0A passes through a certain resistor for 10minutes, $2.88 \times {10^4}J$ of heat is produced. Calculate
A. The power of the resistor
B. The voltage across the resistor

Answer 1

Hint: Resistance: Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohm (Ω). Resistance is also a relationship between current and voltage. Resistor is used to insert the resistance of desire. As we know that resistance is given by:
\[ \Rightarrow R = \dfrac{V}{I}\]
Here
R=resistance
V=voltage
I=current

Complete step by step solution:
Given,
I=4.0A
t=10 minutes
t=600 seconds
H=$2.88 \times {10^4}J$
The power of the resistor
$ \Rightarrow R = \dfrac{V}{I}$$ \Rightarrow H = {I^2}RT$
$ \Rightarrow 2.88 \times {10^4} = {(4)^2} \times R \times 600$
$ \Rightarrow R = \dfrac{{2.88 \times {{10}^4}}}{{16 \times 600}}$
$ \Rightarrow R = 3\Omega $
We know that power is given by
$ \Rightarrow P = {I^2}R$
Put the value in formula
$ \Rightarrow P = {4^2} \times 3$
$ \Rightarrow P = 16 \times 3$
$ \Rightarrow P = 48W$
The voltage across the resistor
$ \Rightarrow V = I \times R$
$ \Rightarrow V = 4 \times 3$
$ \Rightarrow V = 12V$

Note: Voltage is directly proportional to the current. And current is inversely proportional to the resistance higher the current lower the resistance. Resistance also depends on the length, cross-section and properties of material. There are some applications of current to produce heat. Resistors are also made of various types of material and it counts by colour of the resistor.