Resistors in Series and Parallel Introduction In a previous experiment you have experimentally veried Ohm's law (V=IR). Now we will use Ohm's law to study electrical circuits. The components of simple circuits are connected in series and/or parallel. Each component may be represented as a resistance to the ow of current in the circuit. In computing the voltage and current in the circuit (or part of the circuit), it is necessary to know the equivalent resistances of the series and parallel arrangements. In this experiment, the circuit characteristics of resistors in series and parallel will be investigated. After performing this experiment and analyzing the data, you should be able to: 1. Describe the currentvoltage relationships for resistances in series. 2. Describe the currentvoltage relationships for resistances in parallel. Background, Theory and Applications A. Resistances in Series Figure 1. Series circuit Resistors are said to be connected in series when they are connected as in Fig.1. (The resistors are connected in line or "head to tail"). When they are connected to a voltage source V and the switch is closed, the source supplies a current Ito the circuit. By the conservation of charge, this current I ows through each resistor. The voltage drop across each resistor is not equal to V, but the sum of the voltage drops is. V=V1+V2+V3 (1) The voltage drop across each resistor is given by Ohm's law (V = IR) and Eq. 1 may be written as V=V1+V2+V3=IR1+IR2+IR3=I(R1+R2+R3)=IR3 (2) where g. is the equivalent resistance of the resistors in series. That is, the three resistors in series could be replaced by a single resistor with a value of Rs, and the same current I would ow from the source: Rs=R1+Rz+R3 (3) B. Resistances in Parallel Resistors are said to be connected in parallel when connected as in Fig. 2. (In this arrangement, all the \"heads" are connected together, as are all of the "tails"). o - + 0 Junction 1 o Junction 2 Figure 2. Parallel circuit The voltage drops across all the resistors are the same and equal to the voltage V of the source. However, the current I from the source divides among the resistors such that I=II+IZ+I3 (4) The current in an electrical parallel circuit divides according to the magnitudes of the resistances in the parallel branches, i.e. the smaller the resistance of a given branch, the greater the mirrent through that branch. The current through each resistor is given by Ohm's law ( I = V/R,), and Eq.4 may be written as V V V V =.:+:+: