Question

The electrical power flows out of a certain two-terminal element is:

Pₒᵤₜ(t) = i²(t)
where i(t) is the element current.

Determine an expression for the voltage-current relation for the element.

Answer 1

The expression for the voltage-current relation for the element is V(t) = sqrt(i²(t)/R), where V(t) is the voltage across the element, i(t) is the current through the element, and R is the resistance of the element.

Step-by-step explanation:

The expression for the voltage-current relation for the element is given by:

V(t) = sqrt(P0(t)/R)

Where V(t) is the voltage across the element, P0(t) is the power flowing out of the element, and R is the resistance of the element. In this case, P0(t) = i²(t), so the voltage-current relation becomes:

V(t) = sqrt(i²(t)/R)

For example, if the resistance of the element is 10 ohms and the current through the element is 2 amps, the voltage across the element would be:

V(t) = sqrt((2²)/10) = sqrt(0.4) = 0.63 volts