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Resistors in Circuits

There are three things, in Ohm’s Law

1. Resistance
2. Voltage
3. Current

$V=IR$

In this equation if I increases then R will decrease. It means the result of product remain same i.e., V.

If voltage remain constant between two points it means it is balanced by varying the current and resistance together.

If current remains constant between two points or in the circuit it means the ratio of voltage and resistance changed.

Here in this topic we have to determine the total resistance of a circuit by using the Ohm’s law. For this purpose we have to see which parameter is constant between two points voltage or current?

If resistors are in series then voltage changes across each of the resistor. Then total potential difference across all resistors will be the sum of voltages across each resistor.

If resistors are in parallel then current changes across each of the resistor. Then total current in the circuit will be the sum of currents through each register.

So now we will try to find the value of resultant resistance in circuits where resistors are in series and parallel.

Resistors in Series

Figure.1 Resistors in series.

In figure 1, three resistors are connected in series, each resister value is different. The current remain constant means it flows through each resistors uniformly. No change its magnitude.

While potential difference changes across the resistors and observed as V1 , V2 and V3 across the resistor R1, R2 and R3. The total potential difference across the resistors is V. This potential difference is sum of all the potential differences across the resistor R1, R2 and R3.

So we can write

$V=V_{1}+V_{2}+V_{3}$                         ……….(1)

In the above case, according to Ohm’s law

V=IR                                                 ………..(2)

where V is the total potential difference which is equal to the current flowing to product of total resistance in the circuit.

So, we can compare equation one and two,

V=V1+V2+V3

IR=IR1+IR2+IR3

Take I common and cancel out

By this way we will get the resultant resistance of three resistors which were in series. So if the resistors are in series they add algebraically.

 R=R1+R2+R3

If R1=5Ω; R2=2Ω and R3=7Ω

Total R =(5+2+7)Ω=14Ω

NOTE: The actual picture of Ammeter, Voltmeter, Resistor and Cell is shown in Figure 1.