#PARALLEL RESISTANCE SERIES#

The power dissipated by a resistor is equal to ,В and the power supplied by the battery is equal to : Note that the sum of the potential drops across each resistor is equal to the voltage supplied by the battery.Д. The potential drop across each resistor can be found using OhmвЂ™s law:

#PARALLEL RESISTANCE SERIES#

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:Д¬. The equivalent resistance is the algebraic sum of the resistances:Д«. The power supplied by the battery can be found using. The power dissipated by each resistor can be found using ,В and the total power dissipated by the resistors is equal to the sum of the power dissipated by each resistor. The potential drop across each resistor can be found using OhmвЂ™s law. The current through the circuit can be found from OhmвЂ™s law and is equal to the voltage divided by the equivalent resistance.

In a series circuit, the equivalent resistance is the algebraic sum of the resistances. If resistors are connected in series, the equivalent resistance isДЇigureВ 6.2.3В A simple series circuit with five resistors. 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.ДЄny number of resistors can be connected in series. For Figure 6.2.2, the sum of the potential drop of each resistor and the voltage supplied by the voltage source should equal zero: This equation is often referred to as KirchhoffвЂ™s loop law, which we will look at in more detail later in this chapter. According to OhmвЂ™s law, the potential drop across a resistor when a current flows through it is calculated using the equation, where is the current in amps ( ) and is the resistance in ohms ( ).В 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 each resistor, a potential drop occurs that is equal to the loss of electric potential energy as a current travels through each resistor. The current through the circuit depends on the voltage supplied by the voltage source and the resistance of the resistors.

In Figure 6.2.2, the current coming from the voltage source flows through each resistor, so the current through each resistor is the same. (b) The original circuit is reduced to an equivalent resistance and a voltage source. The sum of the individual currents equals the current that flows into the parallel connections.ДЇigureВ 6.2.2В (a) Three resistors connected in series to a voltage source. In the case of a parallel configuration, each resistor has the same potential drop across it, and the currents through each resistor may be different, depending on the resistor. In a parallel circuit, all of the resistor leads on one side of the resistors are connected together and all the leads on the other side are connected together. In a series circuit, the output current of the first resistor flows into the input of the second resistor therefore, the current is the same in each resistor. The simplest combinations of resistors are series and parallel connections ( Figure 6.2.1).

The equivalent resistance of a combination of resistors depends on both their individual values and how they are connected. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistanceВ of the circuit. Most circuits have more than one resistor. Basically, a resistor limits the flow of charge in a circuit and is an ohmic device where. In Current and Resistance, we described the term вЂresistanceвЂ™ and explained the basic design of a resistor.

Calculate the equivalent resistance of resistors connected in parallel.

Calculate the equivalent resistance of resistors connected in series.

By the end of the section, you will be able to:

Parallel resistance