General · correct answers only, in question-pool order.
In a series LC circuit at resonance, inductive and capacitive reactance are equal and opposite, so they cancel. The remaining impedance is therefore very low.
Reactance is the opposition that capacitance or inductance presents to alternating current.
An inductor opposes alternating current through inductive reactance.
A capacitor opposes alternating current through capacitive reactance.
Inductive reactance increases as frequency increases. The relationship is XL = 2πfL.
Capacitive reactance decreases as frequency increases. The relationship is XC = 1/(2πfC).
Admittance is the reciprocal of impedance: Y = 1/Z.
Impedance is the ratio of voltage to current in an AC circuit, combining the effects of resistance and reactance.
Reactance, like resistance and impedance, is measured in ohms.
The official G5A10 source identifies a transformer as one device that can provide impedance matching at radio frequencies.
The official G5A10 source identifies a Pi-network as a circuit that can be used for RF impedance matching.
The official G5A10 source identifies a properly selected length of transmission line as another RF impedance-matching device.
The standard letter used for reactance is X. Inductive reactance is XL and capacitive reactance is XC.
At resonance, inductive and capacitive reactance are equal in magnitude and opposite in sign, so they cancel each other.
A factor-of-two change in power is approximately 3 dB: +3 dB doubles power and -3 dB halves it.
In a parallel circuit, total current is the sum of the currents flowing through the individual branches.
With 400 volts across 800 ohms, power is V²/R = 400²/800 = 200 watts.
Power is voltage times current: 12 V × 0.2 A = 2.4 watts.
Using P = I²R, 0.007² × 1250 is about 0.061 watt, or 61 milliwatts.
A 200-volt peak-to-peak sine wave has 100 volts peak and about 70.7 volts RMS. PEP into 50 ohms is Vrms²/R, which gives 100 watts.
RMS voltage is defined as the AC value that produces the same heating power in a resistor as an equal DC voltage.
For a sine wave, Vpeak = Vrms × √2 and Vpp = 2 × Vpeak. With 120 volts RMS, Vpp is about 339.4 volts.
For a sine wave, Vrms = Vpeak/√2. Seventeen volts peak is therefore about 12 volts RMS.
A 1 dB power loss leaves about 79.4 percent of the original power, which corresponds to a loss of about 20.6 percent.
For an unmodulated carrier, the envelope does not vary, so peak envelope power and average power are equal.
For a 50-ohm load dissipating 1200 watts, Vrms = √(PR) = √(1200×50), or about 245 volts.
An unmodulated carrier has constant envelope amplitude, so its peak envelope power equals its average power: 1060 watts.
A 500-volt peak-to-peak sine wave has 250 volts peak and about 176.8 volts RMS. Squaring that and dividing by 50 ohms gives 625 watts.
An AC current in the primary winding creates a changing magnetic field that induces voltage in the secondary winding. This coupling is mutual inductance.
A transformer works in either direction. Applying the signal to the secondary of a 4:1 step-down transformer makes it operate as a 1:4 step-up transformer, multiplying voltage by four.
For parallel resistors, reciprocals add. 1/10 + 1/20 + 1/50 = 0.17, giving a total resistance of about 5.9 ohms.
For two parallel resistors, R = R1R2/(R1+R2). For 100 and 200 ohms, that gives about 66.7 ohms.
In a voltage step-up transformer, the primary has lower voltage and therefore higher current for roughly the same transferred power. It needs heavier wire to carry that current.
Voltage follows the turns ratio. A 1500-turn secondary has three times the turns of a 500-turn primary, so 120 volts becomes 360 volts.
The impedance ratio of a transformer is the square of the turns ratio. √(600/50) is about 3.46, so a 3.5:1 turns ratio is appropriate.
Parallel capacitances add directly: 5.0 nF + 5.0 nF + 0.750 nF = 10.750 nF.
Three equal capacitors in series have one-third the capacitance of one capacitor. Three 100-microfarad capacitors therefore equal about 33.3 microfarads.
Three equal inductors in parallel have one-third the inductance of one inductor. Three 10-millihenry inductors therefore equal about 3.3 millihenries.
Series inductances add directly: 20 millihenries + 50 millihenries = 70 millihenries.
For two capacitors in series, C = C1C2/(C1+C2). With 20 and 50 microfarads, the result is about 14.3 microfarads.
Adding another capacitor in parallel increases total capacitance because parallel capacitances add directly.
Adding another inductor in series increases total inductance because series inductances add directly.