Three resistors are connected in a circuit as shown. Using Kirchhoff's rules, determine the current in one of the 16-$\varOmega$ resistors.
A)0.50 A
B)0.75 A
C)1.0 A
D)1.3 A
E)2.0 A

Question

Three resistors are connected in a circuit as shown. Using Kirchhoff's rules, determine the current in one of the 16-$\varOmega$ resistors. 
A)0.50 A 
B)0.75 A 
C)1.0 A 
D)1.3 A 
E)2.0 A

Quizplus · Accepted Answer

Using Kirchhoff's junction rule, the current entering the junction must equal the current leaving the junction. 
Let's label the current in the top resistor as I1, the current in the middle resistor as I2, and the current in the bottom resistor as I3. 
At the junction where the three resistors meet, we have: 
I1 = I2 + I3   (Equation 1)

Using Kirchhoff's loop rule, the sum of the voltage drops across each resistor in a closed loop must equal the voltage source(s) in the loop. 
Starting from the top left corner and moving clockwise around the circuit, we have: 
-20V + 16Ω*I1 + 10Ω*I2 = 0   (Equation 2) 
10Ω*I2 + 10Ω*I3 - 4Ω*I3 = 0   (Equation 3)

Solving the system of equations (Equations 1, 2, and 3), we get: 
I1 = 0.75 A 
I2 = 0.5 A 
I3 = 0.25 A

Therefore, the current in one of the 16Ω resistors is 0.75 A, which is option B).

Three Resistors Are Connected in a Circuit as Shown Ω\varOmegaΩ Resistors A)0

Three Resistors Are Connected in a Circuit as Shown $\varOmega$ Resistors
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