P 3.4-3 The ideal voltmeter in the circuit shown in Figure P 3.4-3 measures the voltage v.

Figure P 3.4-3.

(a) Suppose R2 = 6 Ω. Determine the value of R1 and of the current i.

(b) Suppose, instead, R1 = 6 Ω. Determine the value of R2 and of the current i.

(c) Instead, choose R1 and R2 to minimize the power absorbed by any one resistor.

 

(a) Suppose R2 = 6 Ω. Determine the value of R1 and of the current i.

 

So if we know R2, we can find the current in R2

 

 

Now we can find i by using

 

Now apply current division and we can determine R1

 

 

So now we solve for R1

 

 

 

Alternatively, we can find R1 from Ohm’s law

 

 

(b) Suppose, instead, R1 = 6 Ω. Determine the value of R2 and of the current i.

 

We can find i1 from Ohm’s Law

 

In this case that is i also.

 

The current through R2 is again  so we would get again 12 Ω  for R2.

 

(c) Instead, choose R1 and R2 to minimize the power absorbed by any one resistor.

 

To minimize power absorbed by either resistor we need the two resistors to have equal value.  In that case the current in each resistor is equal and must be 1 A each.

 

So from Ohm’s law, we can find R

 

 

Since R2 = R1 = 8 Ω

 

 

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This page last updated on January 18, 2019