Determine resistor R1 in Fig. 6.44 to implement the division of current shown.

Question

Determine resistor [latex]R_1[/latex] in Fig. 6.44 to implement the division of current shown.

Accepted Answer

There are essentially two approaches to this type of problem. One involves the direct substitution of known values into the current divider rule equation followed by a mathematical analysis. The other is the sequential application of the basic laws of electric circuits. First we will use the latter approach.

Applying Kirchhoff’s current law gives

[latex]\sum{I_i}=\sum{I_o}\[0.5cm] I=I_1+I_2\[0.5cm] 27mA=21mA+I_2[/latex]

and [latex]I_2=27mA-21mA=6mA[/latex]

The voltage [latex]V_2: \quad V_2=I_2R_2=(6mA)(7\Omega )=42mV[/latex]

so that [latex]V_1=V_2=42mV[/latex]

Finally, [latex]R_1=\frac{V_1}{I_1}=\frac{42mV}{21mA}=2\Omega[/latex]

Now for the other approach using the current divider rule:

[latex]I_1=\frac{R_2}{R_1+R_2}I_T\[0.5cm] 21mA=\left(\frac{7\Omega }{R_1+7\Omega } \right)27mA\[0.5cm] (R_1+7\Omega )(21mA)=(7\Omega )(27mA)\[0.5cm] (21mA)R_1+147mV=189mV\[0.5cm] (21mA)R_1=189mV-147mV=42mV[/latex]

and [latex]R_1=\frac{42mV}{21mA}=2\Omega[/latex]

Question 6.24: Determine resistor R1 in Fig. 6.44 to implement the division...

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