P 5.6-7 The circuit in Figure P 5.6-7 contains a variable resistance, R, implemented using a potentiometer. The resistance of the variable resistor varies over the range 0 ≤ R ≤ 1000 Ω. The variable resistor can safely receive 1/4 W power. Determine the maximum power received by the variable resistor. Is the circuit safe?

 

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Figure P 5.6-7

 

To find maximum power we must create a Thevenin circuit for rest of circuit other than the variable resistor R.  So we start by removing that and deactivating power sources

So we have two sets of parallel resistances in series.  Start on left

 

 

 

So adding them in series we get Thevenin resistance

 

 

Now we have to find the open circuit voltage between a and b so restoring the power sources we have the circuit

We can find the voltage at each point by using voltage division

 

 

 

So open circuit voltage is

 

 

Since we are determining the max power in variable R the polarity is not important, so we replace R with same value as Rt as that provides maximum power and our circuit can be drawn as

Now power is

We get current from

 

 

 

Yes, Circuit is safe!

 

 

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This page last updated on March 9, 2019