Combination of Resistors
Resistors can be combined in two ways; series and parallel. Combination of more than one resistor is called equivalent resistor. We first look at the resistors in series;
Resistors in Series
![](https://lh3.googleusercontent.com/-wfzFD3dF38E/VpdYV7Lng9I/AAAAAAAAK8I/DV8jkzUJrX8/s330-Ic42/1.png)
a. In this types of circuit, an amount of currents passing through the resistors are equal and this current comes from the battery.
i=i1=i2=i3
b. Sum of the potential differences of each resistor is equal to a total potential difference of the circuit or potential difference between the ends of a battery.
V=V1+V2+V3
c. If ,
V1=i1.R1
V2=i2.R2
V3=i3.R3
V=V1+V2+V3
i.Req=i1.R1=i2.R2=i3.R3
Since the currents are equal to each other;
Req=R1+R2+R3
When you add new resistors to the circuit in series, the equivalent resistance of the circuit increases.
Resistors in Parallel
![](https://lh3.googleusercontent.com/-GsZaNItr1bU/VpdYWGDB5yI/AAAAAAAAK8k/5WP3LiKmWdU/s273-Ic42/2.png)
a. Sum of the currents in each branch is equal to the current coming from the battery.
it=i1+i2+i3
b. Since the two ends of each resistor are connected to the same points, potential differences of each resistor are equal.
V=V1=V2=V3
c.
![](https://lh3.googleusercontent.com/-cPMkaoZ39T4/VpdYWN49r0I/AAAAAAAAK8s/jt4AQBahIs0/s496-Ic42/3.png)
When you add new resistors to the circuit in parallel, the equivalent resistance of the circuit decreases.
d. If n number of resistors are combined in parallel like in the picture given below, we find the equivalent resistance of the circuit as;
![](https://lh3.googleusercontent.com/-umwPDgR0Z-c/VpdYWdhQANI/AAAAAAAAK9A/hhlYvL1dkqo/s303-Ic42/4.png)
Example: Find the equivalent resistance, currents passing through each resistor and the potential difference between the ends of each resistor of the circuit given below.
![](https://lh3.googleusercontent.com/-MB1UkDyWqO4/VpdYWc_fggI/AAAAAAAAK88/dhV-75Gf1Uw/s320-Ic42/5.png)
Since 3Ω and 6Ω resistors are in parallel, their equivalence becomes;
![](https://lh3.googleusercontent.com/-V5ti56o45L8/VpdYWnj40wI/AAAAAAAAK80/iqBAZ7xdxH4/s337-Ic42/6.png)
Since 4Ω and Req1 resistors are in series, their equivalence becomes;
![](https://lh3.googleusercontent.com/-VDkc5WfOhlU/VpdYWtmHLPI/AAAAAAAAK84/J9NfJY6HZ_Y/s361-Ic42/7.png)
Since the equivalent resistance of 3Ω and 6Ω is 2Ω, potential difference between the ends of this resistor is;
V=4A.2Ω=8volt
Currents in the resistors are;
i3=8volt/3Ω=8/3Amper
i6=8volt/6Ω=4/3Amper
i4=4Amper
Potential difference between the ends of the 4Ω resistance is;
V=i.R
V=4A.4Ω=16volt
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