The power, P, dissipated when a 6-volt battery is put across a resistance of R ohms is given by
P=36R.
What is the rate of change of power with respect to resistance?
Ah, the ohm-age-old question of power and resistance! Let's dive into this electrical equation, shall we?
The power, P, dissipated by a 6-volt battery across a resistance of R ohms is given by P = 36R. We want to find the rate of change of power with respect to resistance.
Now, to determine the rate of change, we need to differentiate the power equation with respect to resistance, dP/dR. So, let's dive into it using our electro-comical powers!
Taking the derivative of P = 36R with respect to R, we get:
dP/dR = 36
And there you have it! The rate of change of power with respect to resistance is a whopping 36. So, if you increase the resistance by a teeny-tiny bit, the power will increase by 36 times that amount. That's a electrifyingly large change in power!
I hope this electrifying answer sparked a laugh and illuminated the concept for you!
To find the rate of change of power with respect to resistance, we need to differentiate the equation P = 36R with respect to R.
Taking the derivative of P with respect to R:
dP/dR = d/dR (36R)
Using the power rule of differentiation, where d/dx (ax) = a * (dx)^{a-1}:
dP/dR = 36 * 1
Simplifying, we find that the rate of change of power with respect to resistance is:
dP/dR = 36
To find the rate of change of power with respect to resistance, we need to take the derivative of the power function, P, with respect to resistance, R.
Given that the power function is P = 36R, we can differentiate it using the power rule of differentiation. According to the power rule, if we have a function of the form f(x) = cx^n, where c and n are constants, the derivative of the function with respect to x can be found by multiplying the coefficient of x (c) by the exponent of x (n), and then subtracting 1 from the exponent:
d/dx ( cx^n ) = n * cx^(n-1)
Applying this rule to our power function P=36R, we have:
dP/dR = 36 * 1 * R^(1-1)
Simplifying the expression, we get:
dP/dR = 36
Therefore, the rate of change of power with respect to resistance is a constant value of 36.
dP/dR = 36
That is, if R changes by 1, P changes by 36.