Find the current through R2 in the circuit of Figure 8-20.

Question

Find the current through [latex]R_{2}[/latex] in the circuit of Figure 8-20.

Accepted Answer

Step 1 : Find the current through [latex]R_{2}[/latex] due to [latex] V_{2}[/latex] by replacing [latex]I_{S}[/latex] with an open, as shown in Figure 8-21.

Notice that all of the current produced by [latex]V_{S}[/latex] is through [latex]R_{2}[/latex]. Looking from [latex]V_{S}[/latex],

[latex]R_{T}[/latex]= [latex]R_{1}[/latex] + [latex]R_{2}[/latex] = 320 Ω

The current through [latex]R_{2}[/latex] due to [latex]V_{S}[/latex] is

[latex]I_{2(V_{S})}= \frac{V_{S}}{R_{T}} = \frac{10 \ V}{320 \ \Omega } = 31.2 \ mA[/latex]

Note that this current is upward through [latex]R_{2}[/latex].

Step 2 : Find the current through [latex]R_{2}[/latex] due to [latex] I_{S}[/latex] by replacing [latex]V_{S}[/latex] with a short, as shown in Figure 8-22.

Use the current-divider formula to determine the current through [latex]R_{2}[/latex] due to [latex]I_{S}[/latex].

[latex]I_{2(I_{S})}= \left(\frac{R_{1}}{R_{1}+ R_{2}} \right) I_{S} = \left(\frac{220 \ \Omega }{320 \ \Omega } \right) 100 \ mA = 68.8 \ mA[/latex]

Note that this current also is upward through [latex]R_{2}[/latex].

Step 3 : Both currents are in the same direction through [latex]R_{2}[/latex]. so add them to get the total.
[latex]I_{2(tot)}[/latex] =[latex]I_{2(V_{S})}[/latex] + [latex] I_{2(I_{S})}[/latex]= 31.2 mA + 68.8 mA = 100 mA

Question 8.7: Find the current through R2 in the circuit of Figure 8-20.

Related Answered Questions