Resistance of Charging Circuit from Average Power per Spark Calculator

✖Voltage of power supply Avg pow, is the voltage required to charge a given device within given time.ⓘ Voltage of Power Supply Avg Pow [V_av]			+10% -10%
✖Time Constant avg pow is the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate.ⓘ Time Constant Avg Pow [𝜏_av]			+10% -10%
✖Average power is defined as the ratio of total work done by the body to the total time taken by the body.ⓘ Average Power [P_avg]			+10% -10%
✖Time for charging capacitor to breakdown voltage is denoted by τ.ⓘ Time for Charging Capacitor to Breakdown Voltage [τ_p]			+10% -10%

✖Resistance of the charging circuit avg pow is the resistance of the charging circuit.ⓘ Resistance of Charging Circuit from Average Power per Spark [R_av]

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Formula

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Resistance of Charging Circuit from Average Power per Spark

Formula

`"R"_{"av"} = ("V"_{"av"}^2*"𝜏"_{"av"})/("P"_{"avg"}*"τ"_{"p"})*(1/2-exp(-"τ"_{"p"}/"𝜏"_{"av"})+0.5*exp(-2*"τ"_{"p"}/"𝜏"_{"av"}))`

Example

`"0.180949Ω"=(("10.03V")^2*"100.1s")/("15.7J/s"*"6.001s")*(1/2-exp(-"6.001s"/"100.1s")+0.5*exp(-2*"6.001s"/"100.1s"))`

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Resistance of Charging Circuit from Average Power per Spark Solution

STEP 0: Pre-Calculation Summary

Formula Used

Resistance of the Charging Circuit Avg Pow = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Average Power*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))
R_av = (V_av^2*𝜏_av)/(P_avg*τ_p)*(1/2-exp(-τ_p/𝜏_av)+0.5*exp(-2*τ_p/𝜏_av))
This formula uses 1 Functions, 5 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Resistance of the Charging Circuit Avg Pow - (Measured in Ohm) - Resistance of the charging circuit avg pow is the resistance of the charging circuit.
Voltage of Power Supply Avg Pow - (Measured in Volt) - Voltage of power supply Avg pow, is the voltage required to charge a given device within given time.
Time Constant Avg Pow - (Measured in Second) - Time Constant avg pow is the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate.
Average Power - (Measured in Watt) - Average power is defined as the ratio of total work done by the body to the total time taken by the body.
Time for Charging Capacitor to Breakdown Voltage - (Measured in Second) - Time for charging capacitor to breakdown voltage is denoted by τ.

STEP 1: Convert Input(s) to Base Unit

Voltage of Power Supply Avg Pow: 10.03 Volt --> 10.03 Volt No Conversion Required
Time Constant Avg Pow: 100.1 Second --> 100.1 Second No Conversion Required
Average Power: 15.7 Joule per Second --> 15.7 Watt (Check conversion here)
Time for Charging Capacitor to Breakdown Voltage: 6.001 Second --> 6.001 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_av = (V_av^2*𝜏_av)/(P_avg*τ_p)*(1/2-exp(-τ_p/𝜏_av)+0.5*exp(-2*τ_p/𝜏_av)) --> (10.03^2*100.1)/(15.7*6.001)*(1/2-exp(-6.001/100.1)+0.5*exp(-2*6.001/100.1))

Evaluating ... ...

R_av = 0.180948863181561

STEP 3: Convert Result to Output's Unit

0.180948863181561 Ohm --> No Conversion Required

FINAL ANSWER

0.180948863181561 ≈ 0.180949 Ohm <-- Resistance of the Charging Circuit Avg Pow

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Unconventional machining processes » Electro Discharge Machining (EDM) » System Analysis in EDM » Relaxation Circuit used for Generating Pulses in EDM » Average Power Delivered per Spark » Resistance of Charging Circuit from Average Power per Spark

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Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< 3 Average Power Delivered per Spark Calculators

Voltage of Power Supply from Average Power per Spark

Go Voltage of Power Supply Avg Pow = sqrt((Average Power*Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)/(Time Constant Avg Pow*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))))

Resistance of Charging Circuit from Average Power per Spark

Go Resistance of the Charging Circuit Avg Pow = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Average Power*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))

Average Energy Delivered per Spark

Go Average Power = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Resistance of the Charging Circuit Avg Pow*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow))

Resistance of Charging Circuit from Average Power per Spark Formula

How the spark is produced in Electric Discharge Machining ?

A typical circuit used for supplying the power to an EDM machine is named as the relaxation circuit. The circuit consists of a DC power source, which charges the capacitor ‘C’ across a resistance ‘Rc’. Initially when the capacitor is in the uncharged condition, when the power supply is on with a voltage of Vo, a heavy current, ic, will flow in the circuit as shown to charge the capacitor.The relaxation circuit as explained above was used in the early EDM machines. They are limited to the low material removal rates for fine finish, which limits its application. This can be explained from the fact that the time spent on charging the capacitor is quite large during which time, no machining can actually take place. Thus the material removal rates are low.

How to Calculate Resistance of Charging Circuit from Average Power per Spark?

Resistance of Charging Circuit from Average Power per Spark calculator uses Resistance of the Charging Circuit Avg Pow = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Average Power*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)) to calculate the Resistance of the Charging Circuit Avg Pow, The Resistance of charging circuit from average power per spark formula is defined as the resistance offered by the charging circuit used to charge capacitor of EDM spark circuit. Resistance of the Charging Circuit Avg Pow is denoted by R_av symbol.

How to calculate Resistance of Charging Circuit from Average Power per Spark using this online calculator? To use this online calculator for Resistance of Charging Circuit from Average Power per Spark, enter Voltage of Power Supply Avg Pow (V_av), Time Constant Avg Pow (𝜏_av), Average Power (P_avg) & Time for Charging Capacitor to Breakdown Voltage (τ_p) and hit the calculate button. Here is how the Resistance of Charging Circuit from Average Power per Spark calculation can be explained with given input values -> 0.183483 = (10.03^2*100.1)/(15.7*6.001)*(1/2-exp(-6.001/100.1)+0.5*exp(-2*6.001/100.1)).

FAQ

What is Resistance of Charging Circuit from Average Power per Spark?

The Resistance of charging circuit from average power per spark formula is defined as the resistance offered by the charging circuit used to charge capacitor of EDM spark circuit and is represented as R_av = (V_av^2*𝜏_av)/(P_avg*τ_p)*(1/2-exp(-τ_p/𝜏_av)+0.5*exp(-2*τ_p/𝜏_av)) or Resistance of the Charging Circuit Avg Pow = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Average Power*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)). Voltage of power supply Avg pow, is the voltage required to charge a given device within given time, Time Constant avg pow is the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate, Average power is defined as the ratio of total work done by the body to the total time taken by the body & Time for charging capacitor to breakdown voltage is denoted by τ.

How to calculate Resistance of Charging Circuit from Average Power per Spark?

The Resistance of charging circuit from average power per spark formula is defined as the resistance offered by the charging circuit used to charge capacitor of EDM spark circuit is calculated using Resistance of the Charging Circuit Avg Pow = (Voltage of Power Supply Avg Pow^2*Time Constant Avg Pow)/(Average Power*Time for Charging Capacitor to Breakdown Voltage)*(1/2-exp(-Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)+0.5*exp(-2*Time for Charging Capacitor to Breakdown Voltage/Time Constant Avg Pow)). To calculate Resistance of Charging Circuit from Average Power per Spark, you need Voltage of Power Supply Avg Pow (V_av), Time Constant Avg Pow (𝜏_av), Average Power (P_avg) & Time for Charging Capacitor to Breakdown Voltage (τ_p). With our tool, you need to enter the respective value for Voltage of Power Supply Avg Pow, Time Constant Avg Pow, Average Power & Time for Charging Capacitor to Breakdown Voltage and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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