Phyics
posted by ALan .
A resistor has a resistance R, and a battery has an internal resistance r. When the resistor is connected across the battery, ten percent less power is dissipated in R than would be dissipated if the battery had no internal resistance. Show that the ratio r/R is equal to 0.054
I let R = 1 ohms
r 0.054 ohms
*Without Internal resistance*
Vloop=0
emfIR=0
emf=IR
*With internal resisntace*
Vloop=0
emfIRIr=0
emf=IR+Ir
I get stuck after this, I am unsure where to head now. Can someone please write out the procedure? Please and thank you.

P1 = V^2/R is the power dissipated in R with no internal resistance.
With internal resistance r, the current is V/(R+r) and the power dissipated in R is
P2 = I^2*R = V^2*R/(R+r)^2
If P2/P1 = 0.9,
R^2/(R+r)^2 = 0.9
R/(R+r) = 0.9487
(R+r)/R = 1 + r/R = 1.054
r/R = 0.054 
Thanks a lot!
Respond to this Question
Similar Questions

physics
when you connect an unknown resistor across the terminals of a 1.50 V AAA battery having a negligible internal resistance, you measure a current of 18.0 mA flowing through it .A)what is the resistance of the resistor. B) if you now … 
Ap physics
Four resistors are connected to a battery with a terminal voltage of 12.0 V, (R1 = 40.0 , R2 = 80.0 , R3 = 140.0 and R4 = 15.0 ) (a) Determine the equivalent resistance for the circuit. 1 (b) Determine the current in the battery. 2 … 
physics
Consider a battery that has Vt = 12.0 V when it is not connected to a circuit. When a 10.0 resistor is connected with the battery, the potential difference across the batteryâ€™s terminals drops to 10.9 V. What is the internal … 
Physics
A battery delivering a current of 55.0 A to a circuit has a terminal voltage of 21.8 V. The electric power being dissipated by the internal resistance of the battery is 36 W. Find the emf of the battery. 
Physics
A battery with an emf of 7.9 V and internal resistance of 1.37 Ω is connected across a load resistor R.If the current in the circuit is 0.88 A, what is the value of R? 
Physics
A 79.4Ω and a 47.7Ω resistor are connected in parallel. When this combination is connected across a battery, the current delivered by the battery is 0.296 A. When the 47.7Ω resistor is disconnected, the current from … 
physics
A resistor of resistance R is connected to a power supply of constant EMF E=12 V and internal resistance r=3 Ω . The energy dissipated in the resistor R is used to heat water. What resistance R in Ohms gives the maximum power … 
physics
when a battery is connected to a 100Ω resistor, the current is 4.00 A. When the same battery is connected to a 449Ω resistor, the current is 1.09 A. Find the emf supplied by the battery and the internal resistance of the … 
physics
hen a battery is connected to a 100Ω resistor, the current is 4.00 A. When the same battery is connected to a 449Ω resistor, the current is 1.09 A. Find the emf supplied by the battery and the internal resistance of the … 
Physics
a)In the series circuits, what do you notice about the voltage across each resistor compared with the voltage of the battery?