This is simple to do, but...what are the power requirements of your load? What voltage and current? Any circuit like this always has two parts: one part is producing the 10 second delay, the other part is switching the load.
Actually you may get away without the transistor... the 555 timer is capable of sourcing a surprising amount of current. Take a look at the below wikipedia article on the 555 timer. In monostable mode you can get a 10s pulse and in astable mode you can get a square waveform (repeating 10s pulses) with a selectable duty cycle.
You can certainly use passive components (resistors and capacitors) to do this, but be careful... first of all this won't produce a square wave, the voltage will decrease slowly over time, and the resistance/capacitance required to obtain such a slow droop may not be feasible for your circuit. You could also use an RC circuit and a comparator to determine when 10s is up, but I'd still say the 555 timer is your best option.