Question

Which of the following represents voltage?
A. \[\dfrac{\text{Work done}}{\text{Current }\!\!\times\!\!\text{ Time}}\]
B. $\text{Work done }\!\!\times\!\!\text{ Charge}$
C. $\dfrac{\text{Work done }\!\!\times\!\!\text{ Current}}{\text{Time}}$
D. $\text{Work done }\!\!\times\!\!\text{ Charge }\!\!\times\!\!\text{ Time}$

Answer 1

Hint: We are given four equations and we are asked to find which of the given equations represents voltage. We have three relations between work done and voltage. From those three relations we can formulate the equation for voltage and find which of them is given in the options.

Formula used:
$W=\dfrac{{{V}^{2}}}{R}\times t$ where ‘W’ is the work done, ‘V’ is the voltage, ‘R’ is the resistance and ‘t’ is the time.
$W=VQ$ where ‘W’ is the work done, ‘V’ is the voltage and ‘Q’ is the charge.
$W=VIT$ where ‘W’ is the work done, ‘V’ is the voltage, ‘$I$’ is the current and ‘T’ is the time.

Complete step by step answer:
In the question we are given four relations and we are asked to find which of them represents voltage.
In all the four relations given we can see that ‘Work done’ is common.
Hence we can write all the relations between work done and voltage.
$W=\dfrac{{{V}^{2}}}{R}\times t$, where ‘W’ is the work done, ‘V’ is the voltage, ‘R’ is the resistance and ‘t’ is the time.
From this relation we will get the voltage as,
$\Rightarrow {{V}^{2}}=\dfrac{WR}{t}$
$\Rightarrow V=\sqrt{\dfrac{WR}{t}}$
That is,
\[\Rightarrow \text{Voltage}=\sqrt{\dfrac{\text{Work done }\!\!\times\!\!\text{ Resistance}}{\text{Time}}}\]
Since there is no such relation in the given options we need to consider another relation between work done and voltage.
$W=VQ$, where ‘W’ is the work done, ‘V’ is the voltage and ‘Q’ is the charge.
From this equation we will get the expression of voltage as,
$\Rightarrow V=\dfrac{W}{Q}$, that is
$\Rightarrow \text{Voltage=}\dfrac{\text{Work done}}{\text{Charge}}$
This relation is also not given in the options.
Hence we can consider another relation of work done and voltage.
$W=VIT$, where ‘W’ is the work done, ‘V’ is the voltage, ‘$I$’ is the current and ‘T’ is the time.
From this equation the expression for voltage can be written as,
$\Rightarrow V=\dfrac{W}{I\times T}$, that is,
$\Rightarrow \text{Voltage=}\dfrac{\text{Work done}}{\text{Current }\!\!\times\!\!\text{ Time}}$
Since this relation is given in the options we can say that $\dfrac{\text{Work done}}{\text{Current }\!\!\times\!\!\text{ Time}}$ represents voltage.

So, the correct answer is “Option A”.

Note: Voltage, which is also known as electromotive force, is simply the potential difference in electric charge between two points in an electrical circuit. We know that voltage is also defined as the work done per unit charge in moving charge between two points in an electric field.