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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