###### Advertisements

###### Advertisements

How can three resistors of resistances 2 Ω, 3 Ω and 6 Ω be connected to give a total resistance of (a) 4 Ω, (b) 1 Ω?

###### Advertisements

#### Solution

There are three resistors of resistances 2 Ω, 3 Ω, and 6 Ω respectively.

(a) The following circuit diagram shows the connection of the three resistors.

H

ere, 6 Ω and 3 Ω resistors are connected in parallel.

Therefore, their equivalent resistance will be given by

`1/(1/6+1/3)=(6xx3)/(6+3)=2 Ω`

This equivalent resistor of resistance 2 Ω is connected to a 2 Ω resistor in series.

Therefore, the equivalent resistance of the circuit = 2 Ω + 2 Ω = 4 Ω

Hence the total resistance of the circuit is 4 Ω.

(b) The following circuit diagram shows the connection of the three resistors.

All the resistors are connected in series. Therefore, their equivalent resistance will be given as

`1/(1/2+1/3+1/6)=1/((3+2+1)/6)=6/6=1Omega`

#### APPEARS IN

#### RELATED QUESTIONS

Differentiate between resistances in series and parallel.

Complete the following :-

(b)

Complete the following :-

(c)

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

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 *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?

How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

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

A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistances, which may be used separately, in series, or in parallel. What are the currents in the three cases?

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

A) 24Ω

(B) 100Ω

(C) 50 Ω

(D) 240Ω

Which of the following arrangement, A or B, has the lower combined resistance?

Explain with the help of a labelled circuit diagram, how you will find the resistance of a combination of three resistors of resistances R_{1}, R_{2} and R_{3} joined in parallel.

If current flows through two lamps arranged:

(*a*) in series,

(*b*) in parallel,

and the filament of one lamps breaks, what happens to the other lamp? Explain your answer.

In parallel combination of resistances:

Which of the following combinations have the same equivalent resistance between X and Y?

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.

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 battery of e.m.f. 15 V and internal resistance 2 `Omega` is connected to tvvo resistors of 4 ohm and 6 ohm joined.

(i) In series,

(ii) In para 1 lel. Find in each case the electrica I energy spent per minute in 6 ohm resistor.

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

A cell supplies a current of 1.2 A through two 2Ω resistors connected in parallel. When the resistors are connected in series, if supplies a current of 0.4 A. Calculate the internal resistance and e.m.f of the cell.

Two resistors of resistance 4 Ω and 6 Ω are connected in parallel to a cell to draw 0.5 A current from the cell.

Draw a labeled diagram of the arrangement

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

In the figure below, the ammeter A reads 0.3 A. Calculate:

(i) the total resistance of the circuit

(ii) the value of R

(iii) the current flowing through R.

What connection is used in domestic appliances and why?

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 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.

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:

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

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

The diagram above is a schematic diagram of a household circuit. The house shown in the above diagram has 5 usable spaces where electrical connections are made. For this house, the mains have a voltage of 220 V and the net current coming from the mains is 22A.

- What is the mode of connection to all the spaces in the house from the mains?
- The spaces 5 and 4 have the same resistance and spaces 3 and 2 have respective resistances of 20Ω and 30Ω. Space 1 has a resistance double that of space 5. What is the net resistance for space 5.
- What is the current in space 3?
- What should be placed between the main connection and the rest of the house’s electrical appliances to save them from accidental high electric current?