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Show how you would connect 3 resistors , each of resistance 6

Science

Class 10

NCERT

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How many

176 Ω

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

Show how you would connect 3 resistors , each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm

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?

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Question

Hard

Solving time: 4 mins

Show how you would connect 3 resistors , each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm

Views: 6,453 students

Updated on: Feb 29, 2024

Book:

Science (NCERT)

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Show how you would connect 3 resistors , each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm

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Text solutionVerified

We are given 3 resistors each of resistance

6 Ω

. Equivalent resistance of resistors in series is more than the individual resistance of each resistor while equivalent resistance of resistance in parallel is less than the individual resistance of each resistor.

(i)

To get an equivalent resistance of

9 Ω

, atleast one six ohm resistor should be connected in series with the other resistors.

Since,

R_{e q} = R_{1} + R_{2}

9 = 6 + R_{2}

R_{2} = 3 Ω

⟹ R_{2} < 6 Ω

Connecting the remaining two resistors in parallel will yield an equivalent resistance of

3 Ω

Hence, the first figure shows the configuration of resistors to get equivalent resistor of

9 Ω

(ii)

To get an equivalent resistance of

9 Ω

, no six ohm resistor should be connected in series with the other resistors.

Let one of the branches have only one

6 Ω

resistor.

Since,

\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}

\frac{1}{9} = \frac{1}{6} + \frac{1}{R _{2}}

R_{2} = 12 Ω

Connecting the remaining two resistors in series will yield an equivalent resistance of

12 Ω

Hence, the second figure shows the configuration of resistors to get equivalent resistor of

4 Ω

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How many

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Show how you would connect 3 resistors , each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm

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Question Text	Show how you would connect 3 resistors , each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm
Updated On	Feb 29, 2024
Topic	Electricity
Subject	Science
Class	Class 10
Answer Type	Text solution:1 Video solution: 13
Upvotes	1348
Avg. Video Duration	3 min

Show how you would connect 3 resistors , each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm

Text solutionVerified

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