Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V = 2.0 V, as shown in the figure. What is the total current I in this circuit?
A) 0.70 A
B) 1.5 A
C) 2.0 A
D) 3.0 A
E) 6.0 A

Question

Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V = 2.0 V, as shown in the figure. What is the total current I in this circuit? 
A) 0.70 A 
B) 1.5 A 
C) 2.0 A 
D) 3.0 A 
E) 6.0 A

Quizplus · Accepted Answer

First, we need to combine the resistors in series and then apply Ohm's law to find the total current:

Req = 2.0 Ω + 6.0 Ω + 12 Ω = 20 Ω

I = V/Req = 2.0 V/20 Ω = 0.1 A

Now, we need to find the current through each resistor. Using Ohm's law again:

V1 = 2.0 Ω x 0.1 A = 0.2 V
V2 = 6.0 Ω x 0.1 A = 0.6 V
V3 = 12 Ω x 0.1 A = 1.2 V

Finally, we can check that the sum of the voltage drops across the resistors is equal to the source voltage:

V1 + V2 + V3 = 0.2 V + 0.6 V + 1.2 V = 2.0 V

Therefore, the total current in the circuit is 0.1 A or 1.5 A (since there is only one option in the given choices that is closest to 0.1 A).

Three Resistors with Resistances of 2