Two batteries with emf E1 = 20V and E = 30V and internal resistances r1 = 40 Ohm and r2 = 60 Ohm

| August 8, 2021 | education

Two batteries with emf E1 = 20V and E = 30V and internal resistances r1 = 40 Ohm and r2 = 60 Ohm are connected in parallel. What are the parameters of battery E and r, which can be used to replace these batteries without changing the current in the load?

Let’s find the total internal resistance of two parallel-connected batteries:
Ro = r1 + r2 = 40 + 60 = 100 ohms.
Find the current flowing between two batteries:
I = (E2 – E1) / Ro = (30 – 20) / 100 = 10/100 = 0.1 A.
Let’s find how many volts the voltage on the first battery will increase:
∆E1 = r1 * I = 40 * 0.1 = 4 V.
Let’s find the total voltage of the two batteries:
Uo = ∆E1 + E1 = 4 + 20 = 24 V.
Let’s find the total internal resistance of the two batteries:
Ro = r1 * r2 / (r1 + r2) = 40 * 60 / (40 + 60) = 2400/100 = 24 ohms.
Answer: a battery equivalent to two batteries connected in parallel must have an emf equal to 24 V and an internal resistance equal to 24 ohms.



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