# Parallel resistance and current relationship

### Electrical/Electronic - Series Circuits

Using the flow analogy, electrical resistance is similar to friction. . This is the same as multiplying by , so the relationship between rms The current in a parallel circuit breaks up, with some flowing along each parallel. As you add more and more branches to the circuit the total current will increase because Ohm's Law states that the lower the resistance, the higher the current. For N equal resistors in parallel, the reciprocal sum expression simplifies to: 1 R t o t a l The components divide the current according to their reciprocal The relations for total conductance and resistance stand in a.

With alternating current, the current continually changes direction. This is because the voltage emf is following a sine wave oscillation.

For a wall socket in North America, the voltage changes from positive to negative and back again 60 times each second. You might think this value of V should really be - volts. That's actually a kind of average of the voltage, but the peak really is about V.

### Parallel Circuits

This oscillating voltage produces an oscillating electric field; the electrons respond to this oscillating field and oscillate back and forth, producing an oscillating current in the circuit. The graph above shows voltage as a function of time, but it could just as well show current as a function of time: Root mean square This average value we use for the voltage from a wall socket is known as the root mean square, or rms, average.

- Series and parallel circuits
- Parallel Circuits

Because the voltage varies sinusoidally, with as much positive as negative, doing a straight average would get you zero for the average voltage.

The rms value, however, is obtained in this way: To find the rms average, you square everything to get 1, 1, 9, and Finally, take the square root to get 3.

The average is 2, but the rms average is 3. Doing this for a sine wave gets you an rms average that is the peak value of the sine wave divided by the square root of two.

This is the same as multiplying by 0. If you need to know about the average power used, it is the rms values that go into the calculation.

Series circuits A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: A series circuit is shown in the diagram above.

The current flows through each resistor in turn. If the values of the three resistors are: The current through each resistor would be 0. Parallel circuits A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. 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. 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. 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.

Here's a way to check your answer. If you have two or more resistors in parallel, look for the one with the smallest resistance. The equivalent resistance will always be between the smallest resistance divided by the number of resistors, and the smallest resistance. You have three resistors in parallel, with values 6 ohms, 9 ohms, and 18 ohms.

Circuits with series and parallel components Many circuits have a combination of series and parallel resistors. Generally, the total resistance in a circuit like this is found by reducing the different series and parallel combinations step-by-step to end up with a single equivalent resistance for the circuit. This allows the current to be determined easily. The current flowing through each resistor can then be found by undoing the reduction process.

General rules for doing the reduction process include: Two or more resistors with their heads directly connected together and their tails directly connected together are in parallel, and they can be reduced to one resistor using the equivalent resistance equation for resistors in parallel. Two resistors connected together so that the tail of one is connected to the head of the next, with no other path for the current to take along the line connecting them, are in series and can be reduced to one equivalent resistor.

Nonetheless, when taken as a whole, the total amount of current in all the branches when added together is the same as the amount of current at locations outside the branches. The rule that current is everywhere the same still works, only with a twist. The current outside the branches is the same as the sum of the current in the individual branches.

It is still the same amount of current, only split up into more than one pathway. Throughout this unit, there has been an extensive reliance upon the analogy between charge flow and water flow. Once more, we will return to the analogy to illustrate how the sum of the current values in the branches is equal to the amount outside of the branches.

The flow of charge in wires is analogous to the flow of water in pipes. Consider the diagrams below in which the flow of water in pipes becomes divided into separate branches.

At each node branching locationthe water takes two or more separate pathways. The rate at which water flows into the node measured in gallons per minute will be equal to the sum of the flow rates in the individual branches beyond the node. Similarly, when two or more branches feed into a node, the rate at which water flows out of the node will be equal to the sum of the flow rates in the individual branches that feed into the node. The same principle of flow division applies to electric circuits.

The rate at which charge flows into a node is equal to the sum of the flow rates in the individual branches beyond the node. 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. 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.

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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. 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.

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.