IN AN AC CIRCUIT CONTAINING INDUCTANCE AND CAPACITANCE RESISTANCE NEGLIGIBLE THEN CURRENT AND EMF ARE

in PHASE OR OUT OF PHASE BY WHAT DEGREE EXPLAIN

In an AC circuit that includes inductance and capacitance, while having negligible resistance, the relationship between current and electromotive force (EMF) is quite interesting. In this scenario, the current and EMF are not in phase; instead, they are out of phase by 90 degrees. Let’s break this down to understand why this happens.

The Role of Inductance and Capacitance

In an AC circuit, inductors and capacitors behave differently compared to resistors. An inductor stores energy in a magnetic field when current flows through it, while a capacitor stores energy in an electric field when voltage is applied across it. This fundamental difference leads to a phase shift between the current and voltage in the circuit.

Phase Relationships Explained

In a purely inductive circuit, the current lags the voltage by 90 degrees. This means that when the voltage reaches its maximum value, the current is actually at zero. Conversely, in a purely capacitive circuit, the current leads the voltage by 90 degrees, meaning that the current reaches its maximum value a quarter cycle before the voltage does.

Combining Inductance and Capacitance

When both inductance and capacitance are present in a circuit, the effects of each component interact. In a scenario where resistance is negligible, the circuit can be viewed as a resonant circuit. At resonance, the inductive reactance (which causes the current to lag) and capacitive reactance (which causes the current to lead) cancel each other out. However, if we consider the circuit at a frequency where resonance does not occur, the current will still be out of phase with the EMF.

• Inductive Reactance (XL): This is given by the formula XL = 2πfL, where f is the frequency and L is the inductance. It causes the current to lag.
• Capacitive Reactance (XC): This is calculated as XC = 1/(2πfC), where C is the capacitance. It causes the current to lead.

Resulting Phase Shift

In a circuit with both inductance and capacitance, the overall phase relationship depends on the relative magnitudes of XL and XC. If XL is greater than XC, the current lags the voltage; if XC is greater than XL, the current leads the voltage. However, in the case where resistance is negligible and we are considering the ideal behavior of the circuit, the current and EMF will be out of phase by 90 degrees, with the specific direction of the phase shift depending on whether the circuit is more inductive or capacitive.

Visualizing the Phase Shift

To visualize this, think of a sine wave representing the EMF. The current wave will either peak a quarter cycle (90 degrees) before or after the EMF wave, depending on whether the circuit is predominantly capacitive or inductive. This phase difference is crucial in understanding how energy is transferred and stored in AC circuits.

Conclusion

In summary, in an AC circuit with inductance and capacitance and negligible resistance, the current and EMF are out of phase by 90 degrees. This phase relationship is a direct result of the unique properties of inductors and capacitors, which store and release energy in different ways. Understanding this concept is essential for analyzing and designing AC circuits effectively.