Mathematical relationship for total resistance in a parallel circuit

Series and Parallel Circuits

mathematical relationship for total resistance in a parallel circuit

Components of an electrical circuit or electronic circuit can be connected in many different ways Mathematical descriptions of the electromagnetic field · Electrical The total resistance of resistors in series is equal to the sum of their individual .. The relations for total conductance and resistance stand in a complementary. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: equivalent resistance of resistors. UNDERSTANDING & CALCULATING SERIES CIRCUITS BASIC RULES.

mathematical relationship for total resistance in a parallel circuit

The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total: A parallel circuit is shown in the diagram above.

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In this case the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance. The voltage across each resistor is 10 V, so: A parallel resistor short-cut If the resistors in parallel are identical, it can be very easy to work out the equivalent resistance.

mathematical relationship for total resistance in a parallel circuit

In this case the equivalent resistance of N identical resistors is the resistance of one resistor divided by N, the number of resistors. So, two ohm resistors in parallel are equivalent to one ohm resistor; five ohm resistors in parallel are equivalent to one ohm resistor, etc.

  • Simple Parallel Circuits
  • Series and parallel circuits

This is illustrated in the examples shown below. In the examples a new circuit symbol is introduced - the letter A enclosed within a circle. This is the symbol for an ammeter - a device used to measure the current at a specific point.

mathematical relationship for total resistance in a parallel circuit

An ammeter is capable of measuring the current while offering negligible resistance to the flow of charge. Diagram A displays two resistors in parallel with nodes at point A and point B. Charge flows into point A at a rate of 6 amps and divides into two pathways - one through resistor 1 and the other through resistor 2.

The current in the branch with resistor 1 is 2 amps and the current in the branch with resistor 2 is 4 amps.

mathematical relationship for total resistance in a parallel circuit

After these two branches meet again at point B to form a single line, the current again becomes 6 amps. Thus we see the principle that the current outside the branches is equal to the sum of the current in the individual branches holds true.

Series and parallel circuits - Wikipedia

Four nodes are identified on the diagram and labeled A, B, C and D. Charge flows into point A at a rate of 12 amps and divides into two pathways - one passing through resistor 1 and the other heading towards point B and resistors 2 and 3. The 12 amps of current is divided into a 2 amp pathway through resistor 1 and a 10 amp pathway heading toward point B. At point B, there is further division of the flow into two pathways - one through resistor 2 and the other through resistor 3.

The current of 10 amps approaching point B is divided into a 6-amp pathway through resistor 2 and a 4-amp pathway through resistor 3. Thus, it is seen that the current values in the three branches are 2 amps, 6 amps and 4 amps and that the sum of the current values in the individual branches is equal to the current outside the branches.

Equivalent Resistance The actual amount of current always varies inversely with the amount of overall resistance. There is a clear relationship between the resistance of the individual resistors and the overall resistance of the collection of resistors. Since the circuit offers two equal pathways for charge flow, only one-half the charge will choose to pass through a given branch.

This is the second principle of parallel circuits: The Equation for Parallel Circuits Please note something very important here. In the series circuit, where the total resistance was the sum of the individual resistances, the total was bound to be greater than any one of the resistors individually.

Parallel Circuits

Here in the parallel circuit, however, the opposite is true: Mathematically, the relationship between total resistance and individual resistances in a parallel circuit looks like this: Just as with the series circuit, we can use computer analysis to double-check our calculations. First, of course, we have to describe our example circuit to the computer in terms it can understand.

In a simple parallel circuit, all points are electrically common in one of two sets of points.

mathematical relationship for total resistance in a parallel circuit