Advertisements
Advertisements
Question
With a neat labelled diagram and derive the equation for three resistances connected in parallel.
Solution
When two or more resistors are joined at the same end, the resistances are connected in parallel.
The potential difference in parallel remains the same across all the resistors.
The current is the sum of the currents across all the individual resistors.
l = l1 + l2 + l3 .........(1)
Let Rp be the resultant resistance of the circuit.
On applying Ohm’s law to the entire circuit, we get
l = V/Rp ................(2)
Now, applying Ohm’s law to individual resistances, we get
l1 = V/R1
l2 = V/R2
l3 = V/R3 ................(3)
From equations (1), (2) and (3), we get
`V/R_p=V/R_1+V/R_2+V/R_3`
`therefore1/R_p=1/R_1+1/R_2+1/R_3`
Here, Rp is the resultant resistance. Thus, the reciprocal of the resultant resistance of a parallel combination of resistors is the sum of the reciprocals of individual resistances. The resultant resistance is lesser than all the resistances.
APPEARS IN
RELATED QUESTIONS
What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
How can three resistors of resistances 2 Ω, 3 Ω and 6 Ω be connected to give a total resistance of 4 Ω ?
Find the current in each resistor in the circuit shown below:
In the circuit given below:
(a) What is the combined resistance?
(b) What is the p.d. across the combined resistor?
(c) What is the p.d. across the 3 Ω resistor?
(d) What is the current in the 3 Ω resistor?
(e) What is the current in the 6 Ω resistor?
In the diagram shown below, the cell and the ammeter both have negligible resistance. The resistor are identical.
A wire of resistance R1 is cut into five equal pieces. These five pieces of wire are then connected in parallel. If the resultant resistance of this combination be R2, then the ratio `R_1/R_2` is:
(a) `1/25`
(b)1/5
(c)5
(c)25
Show with the help of diagrams, how you would connect three resistors each of resistance 6 Ω, so that the combination has resistance of (i) 9 Ω (ii) 4 Ω.
State how are the two resistors joined with a battery when equivalent resistance is less than either of the two resistances.
Four resistors each of resistance 2Ω are connected in parallel. What is the effective resistance?
Calculate the equivalent resistance between the points A and B in Fig. if each resistance is 2·0 Ω.
A battery of e.m.f 16 V and internal resistance 2 Ω is connected to two resistors 3Ω and 6Ω connected in parallel. Find:
- the current through the battery.
- p.d. between the terminals of the battery,
- the current in 3 Ω resistors,
- the current in 6 Ω resistor.
A particular resistance wire has a resistance of 3 ohm per meter. Find the potential difference of the battery which gives a current of 2 A in each of the 1.5 m length when connected in the parallel to the battery (assume that resistance of the battery is negligible).
An electrical appliance has a rating 100 W, 120V. The resistance of element of appliance when in use:
The equivalent resistance of a parallel combination of two resistors of 30 Ω and 60 Ω is ______________.
A piece of wire having a resistance R is cut into five equal parts.
- How will the resistance of each part of the wire change compared with the original resistance?
- If the five parts of the wire are placed in parallel, how will the resistance of the combination change?
- What will be ratio of the effective resistance in series connection to that of the parallel connection?
Two devices are connected between two points say A and B in parallel. The physical quantity that will remain the same between the two points is:
Three resistors of 6Ω, 4Ω and 4Ω are connected together so that the total resistance is 8Ω. Draw a diagram to show this arrangement and give reason to justify your answer.
Study the following circuit:
On the basis of this circuit, answer the following questions:
i. Find the value of total resistance between the points A and B.
ii. Find the resistance between the points B and C.
iii. Calculate the current drawn from the battery, when the key is closed
OR
iii. In the above circuit, the 16Ω resistor or the parallel combination of two resistors of 8 Ω, which one of the two will have more potential difference across its two ends? Justify your answer.
Two resistors of resistances 2 Ω and 3 Ω are connected in parallel to a cell to draw current 0.5 A from the cell. Draw a labelled diagram of the arrangement
