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Zorluk: Çok zorVoltage and Electromotive Force (EMF)

An electronics system contains a pulse-forming network where an electromotive force (EMF) source must do 0.24 J0.24\text{ J} of work to move a charge of 2000 \muC2000\text{ \mu C} through the load. The power supply for this system is built by connecting identical 24 V24\text{ V} battery modules in series. Assuming no internal resistance, how many 24 V24\text{ V} battery modules must be connected in series to provide the required EMF?

Cevap: 5 modules

Cevap

5
The total EMF required is found by dividing the work done (0.24 J0.24\text{ J}) by the charge in coulombs (0.002 C0.002\text{ C}), which equals 120 V120\text{ V}. Since each battery module provides 24 V24\text{ V} and they are connected in series, the total EMF is divided by the module voltage. 120 V120\text{ V} divided by 24 V24\text{ V} per module equals exactly 55 modules.

Adım Adım Çözüm

1
Recall the physical definition of electromotive force.
E=WQE = \frac{W}{Q}
EMF is defined as the work done by a source per unit of charge it moves.
2
Convert the given charge into standard SI units (Coulombs).
2000 \muC=2000×10−6 C=0.002 C2000\text{ \mu C} = 2000 \times 10^{-6}\text{ C} = 0.002\text{ C}
Standard units (Joules and Coulombs) are required to calculate voltage in Volts.
3
Calculate the total required EMF.
E=0.24 J0.002 C=120 VE = \frac{0.24\text{ J}}{0.002\text{ C}} = 120\text{ V}
Substituting the work and charge values yields the total potential difference required by the network.
4
Calculate the number of battery modules needed.
120 V/24 V=5120\text{ V} / 24\text{ V} = 5
In a series connection, the total voltage is the sum of the individual voltages, requiring division.

Anahtar Kavram

Electromotive Force (EMF) as Work per Unit Charge and Series Circuit Addition
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Konular

Voltage and Electromotive Force (EMF)

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