With a Neat Labelled Diagram and Derive the Equation for Three Resistances Connected in Parallel. - Science and Technology 1


With a neat labelled diagram and derive the equation for three resistances connected in parallel.



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



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.


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2013-2014 (March)



Differentiate between resistances in series and parallel.

Complete the following :-


Complete the following :-


An electric lamp of 100 Ω, a toaster of resistance 50 Ω, and a water filter of resistance 500 Ω are connected in parallel to a 220 Vsource. 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?

Several electric bulbs designed to be used on a 220 V electric supply line are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?

The equivalent resistance of the parallel combination of two resistors of 60Ω and 40Ω is _______.

A) 24Ω

(B) 100Ω

(C) 50 Ω

(D) 240Ω

A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is the resistance of the combination?

Explain with diagram what is meant by the "series combination" and "parallel combination" of resistances. In which case the resultant resistance is : (i) less, and (ii) more, than either of the individual resistances?

An electric heater which is connected to a 220 V supply line has two resistance coils A and B of 24 Ω resistance each. These coils can be used separately (one at a time), in series or in parallel. Calculate the current drawn when:

(a) only one coil A is used.
(b) coils and B are used in series.
(c) coils and B are uses in parallel.

The figure given below shows three resistors? 


Their combined resistance is: 

(a) `1 5/7`Ω

(b) `14` Ω

(c) `6 2/3` Ω

(d) `7 1/2` Ω

How will you connect three resistors of 2 Ω, 3 Ω and 5 Ω respectively so as to obtain a resultant of 2.5 Ω? Draw the diagram to show the arrangement.

Two resistors having resistance 4𝛀 and 6𝛀 are connected in parallel. Find their equivalent resistance. 

Four resistors each of resistance 2Ω are connected in parallel. What is the effective resistance? 

You have three resistors of values 2Ω, 3Ω and 5Ω. How will you join them so that the total resistance is less than 1Ω? Draw diagram and find the total resistance. 

Calculate the equivalent resistance of the following combination of resistors r1, r2, r3 and r4 if `r_1=r_2=r_3=r_4=2.0Ω ` between the points A and B in Fig. 8.42  



A combination consists of three resistors in series. Four similar sets are connected in parallel. If the resistance of each resistor is 2 ohm, find the resistance of the combination. 

A wire of uniform thickness with a resistance of 27 O is cut into three equal pieces and they are joined in parallel. Find the resistance of the parallel combination.

Show how would you connect three resistors, each of resistance 6 O so that
the combination has a resistance of(a) 9 Ω (b) 4 .Ω

The circuit diagram (Fig .) shows three resistors 2 Ω, 4 Ω and RΩ connected to a battery of e.m.f. 2 V and internal resistance 3 Ω. A main current of 0 .25
A flows through the circuit.

(i ) What is the p.d . across the 4 Ω resistor?
(ii ) Calculate the p.d . across the in ternal resistance of the cell.
(iii ) What is the p.d . across the R Ω or 2 Ω resistors?
(iv) Calculate the value of R.

An electrical appliance having a resistance of 200 Ω is operated at 220 V. calculate the energy consumed by the appliance in 5 minutes in kWh.

The equivalent resistance of a parallel combination of two resistors of 30 Ω and 60 Ω is ______________.

How does the resistance of a metallic wire depend on the length of wire?

What connection is used in domestic appliances and why?

A piece of wire having a resistance R is cut into five equal parts.

  1. How will the resistance of each part of the wire change compared with the original resistance?
  2. If the five parts of the wire are placed in parallel, how will the resistance of the combination change?
  3. What will be ratio of the effective resistance in series connection to that of the parallel connection?

Two resistors when connected in parallel give the resultant resistance of 2 ohms, but when connected in series the effective resistance becomes 9 ohms. Calculate the value of each resistance.

A coil in the heater consumes power P on passing current. If it is cut into halves and joined in parallel, it will consume power:

Three resistors of 1 Ω, 2 Ω and 3 Ω are connected in parallel. The combined resistance of the three resistors should be:

Assertion: When a battery is short circuited, the terminal voltage is zero.

Reason: In a short circuit, the current is zero.

You are given four ammeters A, B, C and D having the least counts mentioned below:

(I) Ammeter A with least count 0.25 A

(II) Ammeter B with least count 0.5 A

(III) Ammeter C with least count 0.05 A

(IV) Ammeter D with least count 0.1 A

Which of the ammeters would you prefer for doing an experiment to determine the equivalent resistance of two resistances most accurately, when connected in parallel?


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