Current Electricity

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Question
CBSEENPH12039825

A cell having an emf and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by

Solution

C.

Here, E = I (R+r) 
E = IR+I
and 
E= V+Ir
straight E space equals straight V plus fraction numerator Er over denominator straight R plus straight r end fraction
straight V equals space straight E minus fraction numerator straight E over denominator straight R plus straight r end fraction xr
straight y space equals space straight c minus 1 over straight x
This equation represents option (c).

Sponsor Area

Question
CBSEENPH12039954

A circuit contains an ammeter, a battery of 30 V and a resistance 40.8 Ω all connected in series. If the ammeter has a coil of resistance 480 Ω and a shunt 20 Ω then reading in the ammeter will be

  • 0.5 A

  • 0.25 A

  • 2 A

  • 1 A 

Solution

A.

0.5 A

Eeffective resistance of a circuit, 


space straight R subscript eff space equals space 40.8 space plus fraction numerator 480 space straight x space 20 over denominator 480 plus 20 end fraction

equals space 40.8 space plus space 19.2 space equals space 60 space straight capital omega
So comma space current space flowing space across space ammeter comma
straight I space equals space space straight V over straight R space equals space 30 over 60 space equals space 1 half space equals space 0.5 space straight A

Hence comma space reading space of space ammeter space equals space 0.5 space straight A

Question
CBSEENPH12040045

A current  of 3 A flows through the 2 Ω resistor shown in the circuit. The power dissiated in the 5 Ω resistor is 

diagram

  • 4 W

  • 2 W

  • 1 W

  • 5 W

Solution

D.

5 W

Voltage across 2 Ω is same as voltage across arm containing 1 Ω and 5 Ω resistance. 
Voltage across 2 Ω resistance, 
V = 2 x 3 = 6 V
So, voltage across lowest arm,
V1 = 6 V
Current across 5 Ω, I = 6/ 1+6 = 1 A
Thus, power across 5 Ω,
P = I2R = (1)2 x 5 = 5 W

Question
CBSEENPH12039920

A current 2 A flows through a 2 Ω resistor when connected across a battery. The same battery supplies a current of 0.5 A when connected across a 9 Ω resistor. The internal resistance of the battery is 

  • 1/3 Ω

  • 1/4 Ω

  • 1 Ω

  • 0.5 Ω

Solution

A.

1/3 Ω

Current space straight i space equals space fraction numerator straight E over denominator straight R space plus straight r end fraction
2 space equals space fraction numerator straight E over denominator straight R space plus straight r end fraction

0.5 space equals space fraction numerator straight E over denominator 2 space plus straight r end fraction space space... space left parenthesis straight i right parenthesis

0.5 space equals space fraction numerator straight E over denominator 9 space plus straight r end fraction.... space left parenthesis ii right parenthesis

From space equation space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space have
fraction numerator 2 over denominator 0.5 end fraction space equals space fraction numerator 9 space plus straight r over denominator 2 space plus space straight r end fraction

3 straight r space equals space 1 space

straight r space equals space 1 third straight capital omega

Question
CBSEENPH12039846

A millivoltmeter of 25 mV range is to be converted into an ammeter of 25 A range. The value (in ohm) of necessary shunt will be

  • 0.001

  • 0.01

  • 1

  • 0.05

Solution

A.

0.001

The full-scale deflection current
straight i subscript straight g equals space fraction numerator 25 space mV over denominator straight G end fraction space ampere
Where G is the resistance of the meter. The value of shunt required for converting it into ammeter of range 25 A is 
space straight S space equals space fraction numerator straight i subscript straight g straight G over denominator straight i minus straight i subscript straight g end fraction
so space that comma space straight S space equals space fraction numerator 25 space mV over denominator 25 end fraction space equals space 0.001 space straight capital omega

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