Question 2.SA.5: Use current division to determine the value of current I1 in......
Use current division to determine the value of current I_1 in the circuit below:
Step-by-Step
We must determine the value of source current I, first. In order to determine the value of current I flowing through the source and the two 5 Ω resistors, we must consolidate all resistors into an equivalent resistance R_{EQ} and then apply Ohm’s law.
R_{EQ}=5 Ω + \left\lgroup\frac{(10 Ω)⋅(10 Ω)}{(10 Ω)+(10 Ω)}\right\rgroup + 5 Ω =5 Ω +5 Ω=15 Ω
I=\frac{V}{R_{EQ}}=\frac{12 V}{15 Ω}=0.8 AApply current division formula in the form of Eq. 2.7:
I_R= \left\lgroup\frac{R_{parallel}}{R_{total}}\right\rgroup⋅I (2.7)
I_{10 Ω}=I_1=\left\lgroup\frac{R_{parallel}}{R_{total}}\right\rgroup⋅I =\left\lgroup\frac{10 Ω}{10 Ω+10 Ω}\right\rgroup⋅(0.8 A)=0.4 ARelated Answered Questions
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