Here Different Resistors are connected between 2 points parallel to each other
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Example
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This is done to decrease net Resistance of Circuit
In this case Total Resistance of circuit is equal to sum of reciprocals of Individual Resistance of the Resistors
1/R = 1/R 1 + 1/R 2 + 1/R 3
IMPORTANT POINTS
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When 2 Resistors are Connected in Parallel
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Different current flow through each resistor but overall Current flowing throughout the circuit remains the Same
Hence we can say that
Total Current = Current flowing through first Resistor + Current flowing through Second Resistor + Current flowing through Third Resistor
I = I 1 + I 2 + I 3
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Potential Difference across allΒ both Resistors remain the same (as they are both between Same points)
Hence we can say that
Potential Diff=V
It is same for both Resistor 1 and Resistor 2
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Now we know that as per Ohm's Law
Potential Diff=Current*Resistance
Potential Difference/Resistance=Current
Current=Potential Diff/Resistance
I = V/R
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How is the Resistance formula Derived - for parallel circuits?
Note - In case of parallel, the total resistance is always less than the resistance of the individual resistors.
The net resistance produced is lowest when resistors are connected in parallel.
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Questions
NCERT Question 5 - How is a voltmeter connected in the circuit to measure the potential difference between two points?
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Q1 Page 216 -
Judge the equivalent resistance when the following are connected in parallel β
(a) 1 β¦ and 10 6 β¦,
(b) 1 β¦ and 10 3 β¦, and 10 6 β¦.
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Q2 Page 216 - An electric lamp of 100 β¦, a toaster of resistance 50 β¦, and a water filter of resistance 500 β¦ are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?
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Q4 Page 216 - How can three resistors of resistances 2 β¦, 3 β¦, and 6 β¦ be connected to give a total resistance of (a) 4 β¦, (b) 1 β¦?
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Q5 Page 216 - What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistance 4 β¦, 8 β¦, 12 β¦, 24 β¦?
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Example 12.8 -
In the circuit diagram given in Fig. 12.10, suppose the resistors R 1 , R 2 and R 3 have the values 5 β¦, 10 β¦, 30 β¦, respectively, which have been connected to a battery of 12 V. Calculate
(a) the current through each resistor,
(b) the total current in the circuit, and
(c) the total circuit resistance.
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Example 12.9 -
If in Fig. 12.12, R 1 = 10 β¦, R 2 = 40 β¦, R 3 = 30 β¦, R 4 = 20 β¦, R 5 = 60 β¦, and a 12 V battery is connected to the arrangement. Calculate
(a) the total resistance in the circuit, and
(b) the total current flowing in the circuit.
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Question 5 - What is the minimum resistance which can be made using five resistors each of 1/5 Ξ©?
(a) 1/5 Ξ©
(b) 1/25 Ξ©
(c) 1/10 Ξ©
(d) 25 Ξ©
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