The figure is not visible in the prompt, so the exact resistor network cannot be reconstructed from the given text alone.

To find the resistance across $ab$ when switches $S_1$ and $S_2$ are closed, I would need the circuit diagram showing:

1. How the resistors are connected,
2. Where $S_1$ and $S_2$ are placed,
3. The resistor values.

Without that figure, the equivalent resistance cannot be derived uniquely from first principles.

However, the stored correct answer is given as $10\,\Omega$. Since no circuit is available to verify independently, the only answer I can report is:

$R_{ab} = 10\,\Omega$

But this is based solely on the provided stored answer, not on a derivation from the circuit.