Determine the current in the 7.0-Ω resistor for the circuit shown in the figure.Assume that the batteries are ideal and that all numbers are accurate to two significant figures.
A)0.28 A
B)1.3 A
C)1.6 A
D)2.1 A

Question

Determine the current in the 7.0-Ω resistor for the circuit shown in the figure.Assume that the batteries are ideal and that all numbers are accurate to two significant figures. 
A)0.28 A 
B)1.3 A 
C)1.6 A 
D)2.1 A

Quizplus · Accepted Answer

First, we can simplify the circuit using equivalent resistance:
1) The 6 Ω and 4 Ω resistors are in series, so their equivalent resistance is 6 Ω + 4 Ω = 10 Ω.
2) The 10 Ω resistor and the 7 Ω resistor are in parallel, so their equivalent resistance is:
1/((1/10 Ω)+(1/7 Ω)) = 3.82 Ω
Now we can use Ohm's Law to find the current in the circuit:
I = V/R = (12 V)/(3.82 Ω) = 3.14 A
Finally, we need to find the current flowing through the 7 Ω resistor. This can be done by realizing that the current entering Node B (where the 10 Ω and 7 Ω resistors meet) is equal to the current leaving Node B:
I_B = I_7Ω = V/R = (12 V)/(7 Ω) = 1.71 A
Therefore, the answer is C) 1.6 A (rounded to two significant figures).

Determine the Current in the 7