An LCR circuit has resistance R₀,inductance L₀,and capacitance C₀.If the resistance value is now tripled,which values of inductance and capacitance will result in the same resonant frequency as before? A)3L₀,C₀ B)L₀/3,C₀/3 C)3L₀,3C₀ D)3L₀,C₀/3

Question

Quizplus · Accepted Answer

The resonant frequency of an LCR circuit is given by f=1/2π√(LC). Since we want to maintain the same resonant frequency after tripling the resistance, the only way to do so is to adjust either the inductance or the capacitance (or both) accordingly.

When the resistance is tripled, the denominator of the formula for resonant frequency is also tripled. To compensate for this, we want to adjust either the inductance or capacitance (or both) by a factor of 1/3 to keep the denominator (LC) the same.

Option D suggests increasing the inductance by a factor of 3 while decreasing the capacitance by a factor of 3. This will keep the product of L and C (and hence the resonant frequency) the same. Therefore, D is the best choice.

An LCR Circuit Has Resistance R0,inductance L0,and Capacitance C0

An LCR Circuit Has Resistance R₀,inductance L₀,and Capacitance C₀