At resonance, bandwidth includes the frequency range that allows _____...
At resonance, bandwidth includes the frequency range that allows 70.2 percent of the maximum voltage to flow. This is because at the bandwidth frequency range, the value of the voltage is equal to the maximum value of voltage divided by √2.
At resonance, bandwidth includes the frequency range that allows _____...
At resonance, the impedance of a circuit is at its minimum value, allowing maximum current to flow. The voltage across the circuit is determined by the impedance and the current flowing through it. Therefore, at resonance, the voltage across the circuit is also at its maximum value.
- At resonance, the circuit is in a state of maximum energy transfer between the source and the load. This means that the circuit is operating at its peak efficiency.
- The bandwidth of a resonant circuit is defined as the range of frequencies around the resonant frequency within which the circuit exhibits a certain level of performance. In the case of voltage, the bandwidth is the range of frequencies over which the voltage across the circuit is within a certain percentage of its maximum value.
- The percentage of the maximum voltage that is considered within the bandwidth is typically defined as a fraction of the maximum voltage. This fraction is often expressed as a decimal value.
- In this case, the correct answer is option 'D', which states that the bandwidth includes the frequency range that allows 70.7% of the maximum voltage to flow.
- This value of 70.7% is derived from the relationship between voltage and current in a resonant circuit. At resonance, the voltage across the circuit is equal to the current multiplied by the impedance. Since the impedance is at its minimum value, the current is at its maximum value.
- The relationship between voltage, current, and impedance in a resonant circuit can be expressed using Ohm's law. V = I * Z, where V is the voltage, I is the current, and Z is the impedance.
- At resonance, the impedance can be represented as a combination of resistance (R) and reactance (X). The reactance can be either inductive (XL) or capacitive (XC), depending on the circuit configuration.
- The impedance magnitude at resonance is given by Z = √(R^2 + (XL - XC)^2). Since the reactance terms cancel out at resonance, the impedance magnitude simplifies to Z = R.
- Therefore, at resonance, the voltage across the circuit is equal to the current multiplied by the resistance. This means that the voltage and current are in phase, and the power factor of the circuit is unity.
- In a resonant circuit, the voltage across the circuit decreases as the frequency moves away from the resonant frequency. The rate at which the voltage decreases depends on the quality factor (Q) of the circuit.
- The bandwidth of the resonant circuit is defined as the range of frequencies on either side of the resonant frequency within which the voltage across the circuit is within a certain percentage of its maximum value.
- The value of 70.7% is derived from the relationship between voltage and power in an AC circuit. The power in an AC circuit is given by P = V^2 / R, where P is the power, V is the voltage, and R is the resistance.
- Since the power is proportional to the square of the voltage, the power is at its maximum value when the voltage is at its maximum value. Therefore, 70.7% of the maximum voltage corresponds to 50% of the maximum power.
- By allowing a range of frequencies within which 70.7% of the maximum voltage can flow, the bandwidth of the resonant circuit ensures that the circuit is operating within an acceptable range of performance.