Prove that the resistance of the infinite network shown below is equal to ( 1 + 3 ) R if each resistance in the network is R .

Since it is an infinite network, equivalent resistance at any point R e q = R + R + ( R | | R e q ) ⇒ R e q = 2 R + R e q × R R e q + R ⇒ R e q = 2 R ( R e q + R ) + R e q R R e q + R = 3 R e q R + 2 R 2 R e q + R ⇒ R e q 2 + R e q R = 3 R e q R + 2 R 2 ⇒ R e q 2 - 2 R e q R - 2 R 2 = 0 ⇒ R e q = R ± 3 R Only positive values will be taken. ⇒ R e q = R ( 1 + 3 ) Hence, proved.

MEDIUM

12th Odisha Board

IMPORTANT

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Find the effective resistance between the points $P$ and $Q$ in the figure given below.

Important Questions on Direct Current Circuits

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 14

Prove that the resistance of the infinite network shown below is equal to $(1 + \sqrt{3}) R$ if each resistance in the network is $R$ .

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EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 15

The reading of high resistance voltmeter, when a cell is connected across it, is $2.2 V$ . When the terminals of the cell are also connected to a resistance of $5 Ω$ , the voltmeter reading drops to $1.8 V$ . Find the internal resistance of the cell.

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12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 16

A battery of emf

E

and internal resistance

r

gives current of

0.5 A

with an external resistance of

12 Ω

and current of

0.25 A

with an external resistance of

25 Ω

. Calculate internal resistance of the cell.

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 16

A battery of emf

E

and internal resistance

r

gives current of

0.5 A

with an external resistance of

12 Ω

and current of

0.25 A

with an external resistance of

25 Ω

. Calculate emf of the cell.

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 17

Use Kirchhoff's law to determine the value of current $I_{1}$ in the electrical circuit given below.

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EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 18

Find the unknown resistance $X$ , in the following circuit, if no current flows through the section $A O$ . Also calculate the current drawn by the circuit from the battery of emf $6 V$ and negligible internal resistance.

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MEDIUM

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 19

Two cells of emf

ε_{1}

and

ε_{2}

have internal resistance

r_{1}

and

r_{2}

. Deduce an expression for equivalent emf of their parallel combination.

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 6 - Direct Current Circuits>MODEL QUESTIONS>Q 20

Twelve cells, each of emf

1.5 V

and internal resistance

0.5 Ω

, are arranged in

m

rows, each containing

n

cells connected in series. Calculate the values of

n

and

m

for which this combination would send the maximum current through external resistance of

1.5 Ω

Find the effective resistance between the points P and Q in the figure given below.

Important Questions on Direct Current Circuits

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Find the effective resistance between the points $P$ and $Q$ in the figure given below.