operational amplifier - How make a dual +-12V supply from a 24V SMPS

I'm trying to power a home-made load cell transmitter using a 24V single SMPS. I need to make +12, 0 and -12 Volts that are capable of 50mA. I wish to power multiple channels of opamps and bridges.

I don't have much budget and availability of components in India.

I have an idea to use 1 LM7812 an 1 LM7912(negative) linear voltage regulators and a voltage divider setup to do this as per the circuit below.

^{simulate this circuit – Schematic created using CircuitLab}

Would this work? I've modified it from the suggestions and articles elsewhere.

Somebody suggested me one other circuit but I am concerned about the current capabilities of the opamp.

^{simulate this circuit}

Would this work? If yes, please suggest suitable op-amp.

Are there any other techniques that would do the job economically?

Answer

You first idea will not work at all.

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Your second idea will work, but many OP-Amps aren't going to deliver more than a few mA on their output, which limits the current your circuit may draw from the virtual ground. There are Power-OP-Amps available which may deliver up to a few ampere, but if you cannot get your hands on one, you can use a PNP/NPN transistor pair to increase the output current:

^{simulate this circuit – Schematic created using CircuitLab}

The OP-Amp will take care of stabilizing the output so it matches the voltage set by the input voltage divider. Take care of capacitive loads, as Spehro noted in his answer, though.