The circuit on the left is CORRECT, if and only if, ...What is the difference between the two circuits?
you use the proper size resistor to allow approx 10ma - 20ma current per LED, or as needed.
Typically, each LED needs it own current limiting resistor because each LED will have slightly DIFFERENT Voltage Drop.
To illuminate all LED's at the same brightness, the LED's will need the same current, this circuit does that = OK.
The circuit one the right is a very POOR design because ...
The LED's will NOT share the current equally because of the above mentioned DIFFERENT "Volt - Amp" characteristics of each LED.
Now, due to the varying current flow in each LED, some LED's may be way too bright and some LED's may be way too dim.
The circuit on the right is forcing EQUAL voltage across each LED, but we know equal voltage does not mean equal brightness.
Each LED must be allowed to have a have a slightly different VOLTAGE.
The circuit on the left - Allows for varying voltages, equal current and equal brightness - GOOD Design
The circuit on the right - Forces equal voltages but varying current and varying brightness - POOR design
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