WHAT IS RESONANCE IN ELECTRICAL CIRCUITS?

Resonance is a phenomenon that occurs when a system is subjected to an external periodic force or vibration that matches its natural frequency, called ‘Resonance frequency’. When this happens, the system absorbs energy efficiently from the external force, causing it to vibrate with much larger amplitude. In other words, a system responds to an external force if the force is at right frequency (the system’s own natural frequency).

In music, to resonate means to make a deep, clear lasting sound. Musical instruments are designed to produce such sounds and notes when activated. Among most common examples are the swing, which has a fixed oscillation time depending on its height, or a tuning fork. Failures of bridges due to matching their frequency with that of marching troops has led to practice of troops breaking their march while crossing a bridge.

Electrical Resonance

When frequency of AC source matches the natural frequency of a circuit, determined by capacitive and inductive elements in circuit, current (or voltage) in circuit becomes much larger than at other frequencies. Energy transfer from source to circuit becomes maximum and highly efficient.  At resonance, voltage (or current) across capacitor and inductor can be much greater than applied voltage (or current). Current and voltage have no phase shift between them, and the circuit becomes purely resistive.

Electrical resonance is essential in radio and TV tuners, filters, oscillators and wireless communication technologies. Resonance is critical for efficient transfer and control of energy in AC circuits and is fundamental in several electrical and electronic applications.

Capacitor and inductor in a circuit may be connected in series or parallel. Accordingly, there are two cases of resonance, viz. Series resonance and parallel resonance. Each of these have their own characteristics and applications.

Inductive reactance is

XL = 2πfL

Capacitive reactance is given by

Both of these are equal (with opposite sign) at resonance. This gives the resonance frequency as

Frequency of AC source matches the natural frequency of the circuit, determined by capacitive and inductive elements in circuit. At this point, current (or voltage) in circuit becomes much larger than at other frequencies. Energy transfer from source to circuit becomes maximum and highly efficient.  At resonance, voltage (or current) across capacitor and inductor can be much greater than applied voltage (or current). Current and voltage have no phase shift between them, and the circuit becomes purely resistive.

Electrical resonance is critical in radio and TV tuners, filters, oscillators and wireless communication technologies. Resonance is critical for efficient transfer and control of energy in AC circuits and is fundamental in several electrical and electronic applications.

Capacitor and inductor in a circuit may be connected in series or parallel. Accordingly, there are two cases of resonance, viz. Series resonance and parallel resonance. Each of these have their own characteristics and applications.

Series Resonance

In the ideal series circuit above, V_L and V_c are in opposite in phase, and dependent on individual values of L and C. Their vectorial addition, or the difference between them, is the supply voltage, as can be visualized. As difference in impedances ωL and 1/ωC narrow down, net impedance reduces, and ideally becomes zero, meaning a direct short circuit. The current in circuit will go dangerously high, ideally becoming infinite. Practically, current is limited by the resistance of inductor coil but is still too large. A resistance is added in series with the circuit, which limits the current at resonance.

Voltages across Inductor and capacitor in series are out of phase by 180 degrees, and at resonance, they are equal and opposite as shown above. The resulting combines voltage across the combination becomes zero, a short-circuit condition. Entire supply voltage appears across a resistance connected in series with the combination, which limits the circuit current.

Parallel Resonance

In the parallel circuit above, both inductor and capacitor get same voltage and draw currents depending on their impedance. Their currents are in opposite phase, and net circuit current is thus a difference of the two currents. At some frequency. Impedances of capacitor and inductor are same, when magnitude of their currents is equal, but opposite in phase. At this point, no current is drawn from circuit, though both capacitor and inductor carry their own individual currents. For the circuit as a whole, impedance is now infinite. A resistor added in parallel limis the minimum current.

The circuit above is often referred as tank circuit. The term comes from its ability to store energy by oscillating back and forth between capacitor and inductor, as it acts as a reservoir for electromagnetic energy, oscillating between electric field (capacitor) and magnetic field (inductor).

Currents in inductor and capacitor are equal and opposite in phase as in figure above. Main circuit current at resonance is zero. This is open circuit condition for voltage source, and circuit current will be decided by any resistance connected in parallel to tank circuit.

Phenomena at or near resonance frequency

Resonance is quite useful in several applications, a few of them being as follows:

• Oscillator circuits
• Radio and Television tuning
• Signal filtering
• Power transmission and wireless power transfer
• Communication systems
• Magnetic resonance technologies like MRI machines
• Instrumentation

Resonance can be dangerous under some conditions

Resonance can be extremely dangerous in certain scenarios.

• Impedances go down drastically in series circuit as resonance frequency approaches. Voltages across capacitors and inductors reach dangerous levels, with damaging effects. It is technically possible to get very high individual component voltages, as high a few thousand volts, using very low supply voltage. This can cause excessive current or voltages, leading to overheating and component damage.
• Broadcasting and EMI issues: Resonance can unintentionally amplify electromagnetic interference, causing malfunction or failure of equipment.
• At resonance, a series LC circuit is like a short circuit, unless protected by a resistance in circuit. In parallel resonance circuits (tank circuits). Currents in both components can go extremely high as resonance frequency approaches.
• At resonance, parallel LC circuit is like an open circuit, drawing no current in an ideal LC circuit. However, currents in components may reach dangerously high, and have to be restricted by resistive components in circuits.
• In power supply systems, resonance can damage whole lines and switchgear, and every measure is taken to avoid the occurrence.
• Efforts are made to avoid resonance in grid system, particularly power factor correction circuits, by use of detuned reactors or other measures, to keep system safe.

Near resonance phenomena is gainfully used in certain applications to get very high voltages or currents from low voltage or low current supply. For instance, circuits are made to get, say, 4400 V AC across capacitor or inductor, using 220 V/ 440 V supply for testing purposes.

In the series LC circuit shown, at power frequency, capacitor and inductor values can be chosen to give voltages as shown. With input voltage of 400 V, capacitor voltage is 4400 V, and inductor voltage 4000 V. This is how large voltages can be generated using LC combination.

Similarly, large currents can be obtained in individual capacitor and inductor in parallel LC circuit, much beyond the capacity of supply source. In the tank circuit above, capacitor and inductor both draw 10 Amp each, while main circuit current is zero, or the circuit sees the tank as open circuit. Resultant current drawn from circuit is zero. This is an open circuit condition for supply. A resistance, when connected in parallel to the combination, decides the circuit current.