Avoltage of 12 cos(i000t+45) vis applied to a circuit in which a resistor of 4 .n, aninductor of l h, and a capacitor of 100 μf are connected in series. if the current in the circuit is in phase with the voltage, find the value of l

0.01 H

Explanation:

V = 12 cos (1000t + 45)

C = 100 micro farad

Let the inductance be L .

When the current and the voltage are in the same phase so it is the condition of resonance.

So capacitive reactance = inductive reactance

Xc = XL

1/ωC = ωL

L = 1 / ω²C

By comparisonV = Vo Cos (ωt + Ф)

ω = 1000 rad/s

L = 1 / (1000 x 1000 x 100 x 10^-6)

L = 1 / 100

L = 0.01H

thus, the inductance of the inductor is 0.01 H.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .