Consider Figure 6. Since there is only one path for the charges to flow through, the current is the same through each resistor. The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of the individual resistances.
In Figure 6. The current through the circuit depends on the voltage supplied by the voltage source and the resistance of the resistors. For each resistor, a potential drop occurs that is equal to the loss of electric potential energy as a current travels through each resistor. Since energy is conserved, and the voltage is equal to the potential energy per charge, the sum of the voltage applied to the circuit by the source and the potential drops across the individual resistors around a loop should be equal to zero:.
For Figure 6. Since the current through each component is the same, the equality can be simplified to an equivalent resistance, which is just the sum of the resistances of the individual resistors.
Any number of resistors can be connected in series. If resistors are connected in series, the equivalent resistance is. One result of components connected in a series circuit is that if something happens to one component, it affects all the other components. For example, if several lamps are connected in series and one bulb burns out, all the other lamps go dark.
A battery with a terminal voltage of is connected to a circuit consisting of four and one resistors all in series Figure 6. Assume the battery has negligible internal resistance. In a series circuit, the equivalent resistance is the algebraic sum of the resistances. The power dissipated by each resistor can be found using , and the total power dissipated by the resistors is equal to the sum of the power dissipated by each resistor. The power supplied by the battery can be found using.
The current through the circuit is the same for each resistor in a series circuit and is equal to the applied voltage divided by the equivalent resistance:. Note that the sum of the potential drops across each resistor is equal to the voltage supplied by the battery.
The power dissipated by a resistor is equal to , and the power supplied by the battery is equal to :. There are several reasons why we would use multiple resistors instead of just one resistor with a resistance equal to the equivalent resistance of the circuit.
Perhaps a resistor of the required size is not available, or we need to dissipate the heat generated, or we want to minimize the cost of resistors. Each resistor may cost a few cents to a few dollars, but when multiplied by thousands of units, the cost saving may be appreciable.
Some strings of miniature holiday lights are made to short out when a bulb burns out. The device that causes the short is called a shunt, which allows current to flow around the open circuit. The bulbs are usually grouped in series of nine bulbs. If too many bulbs burn out, the shunts eventually open. What causes this? Resistors are in parallel when one end of all the resistors are connected by a continuous wire of negligible resistance and the other end of all the resistors are also connected to one another through a continuous wire of negligible resistance.
The potential drop across each resistor is the same. The same is true of the wiring in your house or any building. The current flowing from the voltage source in Figure 6. In this case, the current flows from the voltage source and enters a junction, or node, where the circuit splits flowing through resistors and.
As the charges flow from the battery, some go through resistor and some flow through resistor. The sum of the currents flowing into a junction must be equal to the sum of the currents flowing out of the junction:. There are two loops in this circuit, which leads to the equations and Note the voltage across the resistors in parallel are the same and the current is additive:.
Generalizing to any number of resistors, the equivalent resistance of a parallel connection is related to the individual resistances by. This relationship results in an equivalent resistance that is less than the smallest of the individual resistances. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower.
Three resistors , , and are connected in parallel. The parallel connection is attached to a voltage source. Note that in these calculations, each intermediate answer is shown with an extra digit. The total current is the sum of the individual currents:. Let us use , since each resistor gets full voltage. The general forumula for computing resistance in parallel is:. But this is formula a pain in the neck to work with.
A slightly simpler transformaton, for two resistors, is:. For instance a 30k resistor is not an E12 series value, but you can obtain it by putting two 15k resistors in series to allow a higher voltage. Care should be taken if you pick unequal values.
Divide the voltage by the total resistance to get the current flowing through the resistors, and multiply this current by each of the resistances in turn to get the voltage over this resistor. In the example none of the voltages should exceed 50V.
More power dissipation before the resistors burn. I don't know exactly whether your question contains a trap. If it was, it would be edited by another member to remove the confusion.
Questions have to be as clear as possible. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. I was just wondering about these parallel resistor equations.
Isn't the answer to Task 3 question 1 suppose to be 6 instead of 5. Or am I just totally lost here? Have a good one!
If you don't like the product for whatever reason, send it back packaged and unused for a full refund. Create your account Lost password? First name. Last name. Your cart is empty. Resistors in Series When resistors are connected one after each other this is called connecting in series. This is shown below. To calculate the total overall resistance of a number of resistors connected in this way you add up the individual resistances. Example: To calculate the total resistance for these three resistors in series.
Two Resistors in Parallel To calculate the total overall resistance of a of two resistors connected in this way you can use the following formula: Example: To calculate the total resistance for these two resistors in parallel. Task 2: Calculate the total resistance of the following resistor in parallel. Three or more resistors in parallel To calculate the total overall resistance of a number of three or more resistors connected in this way you can use the following formula: Example: To calculate the total resistance for these three resistors in parallel Task 3: Calculate the total resistance of the following resistor in parallel.
Kitronik's suggested additional learning. Tags: Electronic principles , Understanding components , Understanding principles. Can u guys hep me? Mark Donnison 27 June at pm Hi, without seeing how your classmate is arriving at an answer it is impossible to say.
Thea 17 June at pm Hi!
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