(8%) Problem 11: In order to measure the properties of a battery, several resistors are connected to the battery in series and the terminal voltage is measured. In the first case, the resistor has resistance R1 = 5.5 Γ and the terminal voltage is ΔV1 = 4.6 V. In the second case, the resistor has resistance R2 = 72 Γ and the terminal voltage ΔV2 = 6.5 V.
20% Part (a) Express the current through a battery I using the voltage across the terminal ΔV and the resistance of the circuit R.
I = ΔV/R
20% Part (b) Express the emf of the battery using the variables for current I, internal resistance r, and external resistance R.
ε = I(R + r)
20% Part (c) Express the emf in terms of r, R and ΔV.
ε = ΔV/R (R + r)
20% Part (d) Find the numerical value of r in Ω.
20% Part (e) Find the numerical value of ε in V.