Question

What is the dimension of time in power?

Answer 1

Hint: In science, power is the value of energy carried or transformed per unit of time. In the International Unit system, the power unit is the watt which is equal to one joule per second. Power is sometimes termed activity. Power is a scalar term.

Complete answer:
Power is forever dependent on work performed, so if a person performs work at various rates, his power also changes at various times.
Power is specified as the rate at which work is performed upon a target. Power is a time-based measure. Which is linked to how fast work is done. The formula for power is given by:
$P={\displaystyle \frac{W}{t}}$
W is the work done.
t is the time taken.
And we write work as $W=mgh$
m is the mass,
g is the gravitational acceleration.
h is the height.
Now, formula for power is:
$P={\displaystyle \frac{mgh}{t}}$
Now, we write the formula in terms of dimensions.
$P={\displaystyle \frac{[M][L{T}^{-2}][L]}{[T]}}]$
The dimension formula for power is $[M{L}^2{T}^{-3}]$ .
And here, we can see the power on T is $-3$.
The dimension of time in power is $-3(T^{-3})$.

Note: Power is represented as the rate of performing work; it is the work produced in unit time. The standard unit of power is Watt. Sometimes the power of motor transports and other instruments is provided in Horsepower (hp), which is almost equal to $745.7$ watts.