# Experiment NO.3 Series and parallel connection

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1 Experiment NO.3 Series and parallel connection Object To study the properties of series and parallel connection. Apparatus 1. DC circuit training system 2. Set of wires. 3. DC Power supply 4. Digital A.V.O. meter Theory 1. The Series Circuit A SERIES CIRCUIT or series-connected circuit is a circuit having JUST ONE CURRENT PATH. Thus, Fig.(1) is an example of a series circuit in which a battery of constant potential difference V volts, and three resistances, are all connected in series. There are two ways to connect the resistance 1. Resistance in series When some conductors having resistance R 1 R 2 R 3 etc. are joined end on end as in (fig 3-1 a), these resistances are connected in series. Fig.(1)

2 Since a series circuit has just one current path, it follows that all the components in a series circuit CARRY THE SAME CURRENT I, a fact evident from inspection of Fig.(1). The current I is assumed to be a flow of positive charge, and thus flows out of the positive terminal of the battery and around through the external circuit, reentering the battery at the negative terminal. This is indicated by the arrows in Fig.(1). In a series circuit, the TOTAL resistance, R T, that the battery sees is equal to the SUM of the individual resistances. Thus, in the particular case of Fig.(1) the battery sees a total resistance, R T = R1 + R2 + R3, while in the general case of n resistances connected in series the battery sees a total resistance of : R T = R1 + R2 + R3 Rn.. + By Ohm s law, it follows that the current I in a series circuit is equal to Resistance, on the other hand, consumes electrical energy, removing it from the circuit in the form of heat. Since resistance does not produce or generate electrical energy, it is a non-active or PASSIVE type of circuit element. The potential difference between the terminals of a resistor is called the VOLTAGE DROP across the resistor, and, is equal to the current I times the resistance R; that is, the voltage drop across a resistance of R ohms carrying a current of I amperes is I R volts. We have the important fact that: In a series circuit, the applied voltage is equal to the sum of the voltage drops.

3 It should be pointed out that the voltage drop across a resistor is always from plus to minus in the direction of the current flow, a fact illustrated in Fig.(2). Fig.(2) 2. The Parallel Circuit A PARALLEL circuit is one in which the battery current divides into a number of parallel paths. This is shown in Fig.(3), in which a battery, of constant V volts, delivers a current of I amperes to a load consisting of any number of n resistances connected in parallel. Fig.(3)

4 The currents in the individual resistances are called the branch currents, and the battery current I is often called the line current. From inspection of Fig.(3) we see that, in a parallel circuit, the battery current I is equal to the sum of the branch currents. If the battery voltage V is applied equally to all n resistances; that is, the same voltage V is applied to all the parallel branches. Hence, by Ohm s law, the individual branch currents in Fig.(3) have the values: Then, we have: Now let R T be the total resistance as seen by the battery in Fig.(3). Then, by Ohm s law, it has to be true that: Since the left-hand sides of the last two equations are equal, the two righthand sides are also equal. Setting the two right-hand sides equal, then canceling the Vs, gives

5 Procedure 1. Using the DC circuit trainer, connect the circuit Shown in Fig. (4), take V T =10V, and R 1 =82Ω, R 2 = 100Ω and R 3 =150Ω. 2. Measured the voltage and current of "R 1, R 2 & R 3 ", then record it in table below V(volt) V T = I(mA) I T = 3. By using ohm's law, Calculate the R T 4. Disconnect the DC power supply, and then measured the equivalent resistance by using the AVO meter only V V V V Fig.(4) 5. Using the DC circuit trainer, connect the circuit Shown in Fig.(5), and take V T =10V, and R 1 =82Ω, R 2 = 100Ω and R 3 =150Ω. 6. Measured the voltage and current of "R 1, R 2 & R 3 ", then record it in table below

6 7. Disconnect the DC power supply, and then measured the equivalent resistance by using the AVO meter only I (ma) I T = V(volt) V T = 10V Discussion Fig.(5) 1. Tow resistors (R 1, R2) are connect in parallel, prove that R T = R 1 R2 R 1 + R 2 2. For the circuit shown below, find R T, V 2.

7 3. In Figure, the battery voltage is V = 65 volts, and the values of the resistances, in ohms, are 38, 17, and 27, as shown. Find: (a) Total resistance seen by the battery, (b) Current measured by the ammeters shown in the figure, (c) Power output of the battery, (d) Power input to each resistor.

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