Question

Choose all correct sentences a. The power (equation 8) is maximum when the value of the impedance is greater than the value of the resistance. b. Resonance occurs when ω2 = 1/ LC c. At resonance, the power is maximum and the impedance is minimum. d. At resonance, R2- LC e. The quality factor L/ C f. The quality factor Q = g. The impedance Z is always larger than the resistance R.

Answer 1

Note: Check the attached image for a clearer question

From the attached image, the answers are 2,3,6,7

Step-by-step explanation:

Maximum power occurs at resonance, i.e.
`X_(L) = X_(C)`, not when impedance is greater than resistance

Resonance occurs when the Inductive reactance equals the capacitive reactance, i.e.
`X_(L) = X_(C)`, not
`R^(2) = (X_(L) - X_(C) ) ^(2)`

and when,
`w = (1)/(√(LC) )`

Therefore, option B is correct

Since the formula for impedance is
`Z = \sqrt{R^(2) + (X_(L)-X_(C)) ^(2) }`, at resonance, Z = R i.e. the impedance is minimum

At resonance, there is maximum power and minimum impedance

Thew Quality Factor,
`Q = (w_(0)L )/(R) = (1)/(R) \sqrt{(L)/(C) }`

The impedance Z is always larger than the resistance R, note that it is not stated that this condition is at Resonance, that makes it correct.

`Z = \sqrt{R^(2) + X^(2) }`