Series Circuit Problem Solving

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These two laws are directly involved in all electrical phenomena and will be invoked repeatedly to explain both specific effects and the general behavior of electricity. (Note that the same amount of charge passes through the battery and each resistor in a given amount of time, since there is no capacitance to store charge, there is no place for charge to leak, and charge is conserved.) Now substituting the values for the individual voltages gives This implies that the total or equivalent series resistance of three resistors is . (c) Calculate the voltage drop in each resistor, and show these add to equal the voltage output of the source.Various parts are identified as either series or parallel, reduced to their equivalents, and further reduced until a single resistance is left. This combination of seven resistors has both series and parallel parts.Each is identified and reduced to an equivalent resistance, and these are further reduced until a single equivalent resistance is reached.The sum of these voltages equals the voltage output of the source; that is, This equation is based on the conservation of energy and conservation of charge.Electrical potential energy can be described by the equation , where is the electric charge and is the voltage.Each resistor draws the same current it would if it alone were connected to the voltage source (provided the voltage source is not overloaded).For example, an automobile’s headlights, radio, and so on, are wired in parallel, so that they utilize the full voltage of the source and can operate completely independently. (See [link](b).) To find an expression for the equivalent parallel resistance , let us consider the currents that flow and how they are related to resistance.Thus, Discussion for (d) The power dissipated by each resistor is considerably higher in parallel than when connected in series to the same voltage source.Strategy and Solution for (e) The total power can also be calculated in several ways.[link] shows resistors in series connected to a source.It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence.


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