Voltage Sources in Parallel

Because the voltage is the same across parallel elements,
voltage sources can be placed in parallel only if they have the same voltage.
The primary reason for placing two or more batteries or supplies in parallel is to increase the current rating above that of a single supply. For example, in Fig. 1, two ideal batteries of 12 V have been placed in parallel. The total source current using Kirchhoff's current law is now the sum of the rated currents of each supply. The resulting power available will be twice that of a single supply if the rated supply current of each is the same. That is,
with $I_1 = I_2 = I$ then
$$P_T = E(I_1 + I_2)$$ $$= E(I + I) = E(2I) $$ $$= 2(EI) = 2P$$
Fig. 1: Examining the impact of placing two lead-acid batteries of different terminal voltages in parallel.
If for some reason two batteries of different voltages are placed in parallel, both will become ineffective or damaged because the battery with the larger voltage will rapidly discharge through the battery with the smaller terminal voltage. For example, consider two lead acid batteries of different terminal voltages placed in parallel as shown in Fig. 2. It makes no sense to talk about placing an ideal 12 V battery in parallel with a 6 V battery because Kirchhoff's voltage law would be violated. However, we can examine the effects if we include the internal resistance levels as shown in Fig. 2.
Fig. 2: Examining the impact of placing two lead-acid batteries of different terminal voltages in parallel.
The only current-limiting resistors in the network are the internal resistances, resulting in a very high discharge current for the battery with the larger supply voltage. The resulting current for the case would be
$$ I = {E_1 - E_2 \over R_{int1} + R_{int2}}$$
$$= {12 V - 6 V \over 0.03 Ω + 0.02 Ω}$$
$$ = {6 V \over 0.05 Ω} = 120 A$$
This value far exceeds the rated drain current of the $12 V$ battery, resulting in rapid discharge of $E_1$ and a destructive impact on the smaller supply due to the excessive currents. This type of situation did arise on occasion when some cars still had $6 V$ batteries. Some people thought, If I have a $6 V$ battery, a $12 V$ battery will work twice as well "not true"!
In general,
it is always recommended that when you are replacing batteries in series or parallel, replace all the batteries.
A fresh battery placed in parallel with an older battery probably has a higher terminal voltage and immediately starts discharging through the older battery. In addition, the available current is less for the older battery, resulting in a higher-than-rated current drain from the newer battery when a load is applied.

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