P 5.4-13 The circuit shown in Figure P 5.4-13 consists of two parts, the source (to the left of the terminals) and the load. The load consists of a single adjustable resistor having resistance 0 ≤ R_L ≤ 20 Ω. The resistance R is fixed, but unspecified. When R_L = 4 Ω, the load current is measured to be i_o = 0.375 A. When R_L = 8 Ω, the value of the load current is i_o = 0.300 A.

(a) Determine the value of the load current when R_L = 10 Ω.

(b) Determine the value of R.

Figure P 5.4-13

First let’s replace non-load part of circuit with a Thevenin equivalent circuit. So first deactivate the power source and the circuit becomes:

Now find R_eq

Next find the open circuit voltage for

is the voltage across the resistor R which is result of current flowing through it.

So our circuit is now

So solve for i_L

Now solve for R in terms of i_L

Collect R terms

Now make use that

Check R value using

Now find i_L when R_L is 10 Ω

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This page last updated on March 7, 2019