Three resistors connected in parallel have individual values of 4.0,6.0 and 10.0 Ω,respectively.If this combination is connected in series with a 12-V battery and a 2.0-Ω resistor,what is the current in the 10-Ω resistor?
A) 0.59 A
B) 1.0 A
C) 11 A
D) 16 A

Question

Three resistors connected in parallel have individual values of 4.0,6.0 and 10.0 Ω,respectively.If this combination is connected in series with a 12-V battery and a 2.0-Ω resistor,what is the current in the 10-Ω resistor? 
A) 0.59 A 
B) 1.0 A 
C) 11 A 
D) 16 A

Quizplus · Accepted Answer

First, we need to find the equivalent resistance of the three resistors in parallel:
1/R_eq = 1/4 + 1/6 + 1/10
1/R_eq = 15/60
R_eq = 4 Ω

Next, we can find the total resistance of the circuit:
R_tot = R_eq + 2 Ω + 10 Ω
R_tot = 16 Ω

Using Ohm's law, we can find the current in the circuit:
I = V/R_tot
I = 12 V/16 Ω
I = 0.75 A

Since the resistors are in series, the current through each resistor is the same. Therefore, the current in the 10-Ω resistor is also 0.75 A.

However, this is not one of the answer choices. To find the closest answer choice, we can round the current to the nearest tenth:
0.75 A ≈ 0.8 A
0.8 A is closest to answer choice A (0.59 A), so that is the best choice.

Three Resistors Connected in Parallel Have Individual Values of 4