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In Fig. E26.11, the battery has emf 35.0 V and negligible internal resistance. R1=5.00Ω. The current through is R1, 1.5 A and the current through R3is 4.50 A. What are the resistances R1and R3?

Short Answer

Expert verified

The value of resistances isR2=2.5Ω and R3=6.11Ω.

Step by step solution

01

Definition of Internal Resistance

Internal resistance refers to the opposition to the flow of charges offered by the cells and batteries themselves resulting in the generation of heat.

02

Determine the resistance R2

Given data:

  • ε=35.0V
  • I3=4.5A
  • I1=1.5A
  • r = 0

AsR1 andR2 are in parallel, this means they have the same voltage that equals to the voltage across their combination R12. So, the voltage acrossR2 is given using Ohm’s law as:

V2=V1=I1R1

Plug the values,

V2=1.5A5.0Ω=7.5V

Now, the combination is in series with , which means the current is the same for both as:

I3=I12=I1+I2

Plug the values,

l2=l3-l1=4.5-1.5=3.0A

Now, use Ohm’s law to calculate resistance as:

R2=V2l2=7.53.0=2.5Ω

03

Determine the resistance R3

The voltage drop of the battery is due to R3and the combination R12. And as the internal resistance is zero, the Ohm's law can be used as:

ε=I(R12+R3)R3=εl=R12 (1)

The combination can be calculated as:

R12=R1R2R1+R2=5.02.55.0+2.5=1.67Ω

Plug the values in equation (1),

R3=35.0V4.5A-1.67Ω=6.11Ω

Thus, the value of resistances is R2=2.5Ωand R3=6.11Ω.

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