Minimized pure resistance, R, arm BC resistance of 800 ohms in parallel with a capacitor of 0.5uF;
arm CD, a resistance of 400 ohms in series with a capacitor of 1.0uF; and arm DA, a
resistance 1000 ohms.
(1) Obtain the value of the frequency for which the bridge can be balanced by first
deriving the balance equations connecting the branch impedance and
(ii) Calculate the value of the resistance in arm AB to produce balance.​

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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 .