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Question

Two batteries with e.m.f. 12V and 13V are connected in parallel across a load resistor of 10Ω. The internal resistances of the two batteries are 1Ω and 2Ω respectively. The voltage across the load lies between.


  1. 11.4V and 11.5V

  2. 11.7V and 11.8V

  3. 11.6V and 11.7V

  4. 11.5V and 11.6V

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Solution

The correct option is D

11.5V and 11.6V


Step 1: Given Data

Emf of the first battery E1=12V

Emf of the second battery E2=13V

The internal resistance of the first battery r1=1Ω

The internal resistance of the second battery r2=2Ω

Resistance of the resistor R=10Ω

Step 2: Formula Used

Equivalent resistance Eeq=E1r1+E2r21r1+1r2

Ohm's law, V=IR

Step 3: Calculate Equivalent EMF

We know that the equivalent resistance is given as,

Eeq=E1r1+E2r21r1+1r2=121+13211+12

=24+132+1=373

Step 4: Calculate Equivalent Resistance

Their equivalent internal resistance is given as,

1req=1r1+1r2=1+12=32req=23Ω

Therefore, req and R resistance is present in series, which gives the total equivalent resistance as,

Req=R+req=10+23=323Ω

Step 5: Calculate the Voltage

According to Ohm's law,

I=EeqReq=373323=3732A

Therefore, the voltage across the resistance R,

V=IR=3732×10=11.5V

Hence, the correct answer is option (D).


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