suppose u have an unlimited supply of 1 watt, 100 ohms and you need to get a100 ohm 10 watt resistor this can be done most cheaply by means of a series parallel matrix of ?.......the answer is 4x4 resistor but why and how??
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Each series of four resisters makes 400 ohms
parallel resistances are figured by taking the reciprocal of the sums of the reciprocals so
the left two sets of 400 ohm resisters in parallel make 200 ohms
likewise the right two sets of 400 resisters also make a 200 ohm setup
adding the two 200 ohm setups together give the desired 100 ohm total resistance
so four parallel sets of four 100 ohm resistances in series give you 100 ohms
now for power capacity
each resistor in a series of 4 will handle the same current
at a fixed voltage, the current through a single 100 ohm resistor will also appear across the four parallel sets of resistors equaling 100 ohms
so each of the four parallel branches will carry 1/4 of the current.
as power is current squared times resistance
and the resistance of each individual resistor is constant at 100 ohms
by reducing the current to 1/4, we have reduced the power to 1/16
Our 4 X 4 matrix of 1 watt resistors is capable of handling 16 watts of power. Well above our desired consumption of 10 watts.
through putting the three 6K ohm resistors in parallel you're making a resistor equivalent of 2K ohm. putting that right into a sequence configuration with the 3K ohm resistor will bring about the final value you have asked for. Reminder that resistors in sequence upload, in parallel the reciprocals upload (a million/Rt = a million/R1 + a million/R2).