An RLC series circuit is driven by a sinusoidal emf with angular frequency _d.If _d is increased without changing the amplitude of the emf, the current amplitude increases.If L is the inductance, C is the capacitance, and R is the resistance, this means that: A)" _dL 1/ _dC" B)" _dL R" E)" _dL

Question

An RLC series circuit is driven by a sinusoidal emf with angular frequency _d.If _d is increased without changing the amplitude of the emf, the current amplitude increases.If L is the inductance, C is the capacitance, and R is the resistance, this means that: A)" _dL > 1/ _dC" B)" _dL < 1/ _dC" C)" _dL = 1/ _dC" D)" _dL > R" E)" _dL < R"

Quizplus · Accepted Answer

The resonance angular frequency of the circuit is given by ω0=1/√(LC). At resonance, the impedance of the circuit is purely resistive and given by R. When the driving angular frequency ω is increased, the impedance of the circuit increases, and the current amplitude decreases. Therefore, to increase the current amplitude as stated in the question, the angular frequency must be decreased, which can be achieved by increasing either the inductance L or the capacitance C. Using the resonance formula, we have ω0=1/√(LC), which can be rearranged to give L/C=1/ω0^2. If ω is decreased while keeping the amplitude of the emf constant, then ω/ω0<1, which means that L/C<1/ω^2. This can be rewritten as L<1/(Cω^2), which means that L<1/(F1^2C). Therefore, the correct answer is B, which states that ωL<1/ωC or equivalently L<1/(F1^2C).

An RLC Series Circuit Is Driven by a Sinusoidal Emf