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Lesson 7: Parallel Voltage Sources and the Current Divider Rule

Lesson 7: Parallel Voltage Sources and the Current Divider Rule. Learning Objectives. Demonstrate how to calculate the total current and branch currents in a parallel circuit using the current divider equation.

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Lesson 7: Parallel Voltage Sources and the Current Divider Rule

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  1. Lesson 7: Parallel Voltage Sources and the Current Divider Rule

  2. Learning Objectives • Demonstrate how to calculate the total current and branch currents in a parallel circuit using the current divider equation. • Describe the effect of connecting DC voltage sources (e.g. battery) in series and in parallel. • Determine the net effect of parallel combining voltage sources. • Compute the power dissipated by each element in a parallel circuit, and calculate the total circuit power.

  3. CURRENT DIVIDER RULE • For series circuits we have the voltage divider rule for finding the voltage across a resistor in a series circuit. • We now introduce the current divider rule (CDR) for finding the current through a resistor in a parallel circuit.

  4. CURRENT DIVIDER RULE • In general: • For two parallel elements of equal value, the current will divide equally. • For parallel elements with different values, the smaller the resistance, the greater is the share of input current. • For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistance values.

  5. CURRENT DIVIDER RULE • Note also that for a parallel network, the current through the smallest resistor will be very close to the total entering current if the other parallel elements of the configuration are much larger in magnitude.

  6. Consider the current i1 and i2 through two resistors in parallel. The total current i is shared by the resistors in inverse proportion to their resistances. “More current follows the path of least resistance.” Principle of current division

  7. Extreme cases for current division short circuit open circuit

  8. Current Divider Rule • Allows us to determine how the current flowing into a node is split between the various parallel resistors

  9. Resistors in Parallel • Remember how to calculate total resistance for resistors in parallel:

  10. Current Divider Rule

  11. Current Divider Rule • For only two resistors in parallel:

  12. Current Divider Rule • If current enters a parallel network with a number of equal resistors, current will split equally between resistors • In a parallel network, the smallest value resistor will have the largest current

  13. Example Problem 1 Use the current divider rule to determine all unknown currents:

  14. Battery cells in series vs parallel Cells connected in series increases available voltage. Cells connected in parallel increases available current.

  15. Voltage Sources in Parallel • When two equal sources are connected in parallel • Each source supplies half the required current

  16. FIG. 6.46 Demonstrating the effect of placing two ideal supplies of the same voltage in parallel. VOLTAGE SOURCES IN PARALLEL

  17. VOLTAGE SOURCES IN PARALLEL • Because the voltage is the same across parallel elements, voltage sources can be placed in parallel only if they have the same voltage. • The primary reason for placing two or more batteries or supplies in parallel is to increase the current rating above that of a single supply.

  18. Voltage Sources in Parallel • Voltage sources with different potentials should never be connected in parallel • Large currents can occur and cause damage

  19. FIG. 6.47 Examining the impact of placing two lead-acid batteries of different terminal voltages in parallel. VOLTAGE SOURCES IN PARALLEL • If for some reason two batteries of different voltages are placed in parallel, both will become ineffective or damaged because the battery with the larger voltage will rapidly discharge through the battery with the smaller terminal voltage.

  20. VOLTAGE SOURCES IN PARALLEL • In general, it is always recommended that when you are replacing batteries in series or parallel, replace all the batteries.

  21. Analysis of Parallel Circuits • Voltage across all branches is the same as the source voltage • Determine current through each branch using Ohm’s Law • Find the total current using Kirchhoff’s Current Law

  22. Example Problem 2 • Determine all unknown currents and total resistance. • Verify KCL for node a

  23. Power Calculations • To calculate the power dissipated by each resistor, use either VI, I2R, or V2/R • Total power consumed is the sum of the individual powers • Compare with IT2RT

  24. Example Problem 3 • Solve for indicated currents. • Determine power dissipated by each resistor • Verify total power = sum of all power dissipated

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