# Voltage and frequency during testing of 10kV cables using a Variable Frequency AC Resonant Test System

According to the characteristics of series resonant circuits, when a 10kV cable is tested using a variable frequency series resonant testing System, the relationship between voltage and frequency can be calculated using the following formula:

1. Resonance frequency of series resonant circuit $f-0 $:

$$f0=\ frac {1} {2 \ pi \ sqrt {LC}}$$

Among them, $L $is the inductance of the series resonant circuit, and $C $is the capacitance of the series resonant circuit.

2. Voltage of series resonant circuit V:

$$V=\ frac {V_ {\ text {input}} {\ sqrt {1+(\ frac {f} {f0} - \ frac {f0} {f}) ^ 2Q ^ 2}$$

Among them, $V_ {\ text {input}} $is the input voltage, $f $is the test frequency, and $Q $is the quality factor of the circuit.

Therefore, based on the above formula, the voltage and frequency of the 10kV cable during testing in a frequency conversion series resonance test device can be calculated.

1. Resonance frequency of series resonant circuit $f-0 $:

$$f0=\ frac {1} {2 \ pi \ sqrt {LC}}$$

Among them, $L $is the inductance of the series resonant circuit, and $C $is the capacitance of the series resonant circuit.

2. Voltage of series resonant circuit V:

$$V=\ frac {V_ {\ text {input}} {\ sqrt {1+(\ frac {f} {f0} - \ frac {f0} {f}) ^ 2Q ^ 2}$$

Among them, $V_ {\ text {input}} $is the input voltage, $f $is the test frequency, and $Q $is the quality factor of the circuit.

Therefore, based on the above formula, the voltage and frequency of the 10kV cable during testing in a frequency conversion series resonance test device can be calculated.