Explanation:
Resistors in series are added together. The total resistance is greater than the individual resistances. Resistors in parallel are inversely added. The total resistance is less than the individual resistances. Ohm's law says that the voltage across a resistor is equal to the current through the resistor times its resistance.
First, we need to use the 4 band color code to find the resistance of each resistor. The first two bands are the first and second digits, the third band is the multiplier, and the fourth band is the tolerance.
Brown-black-brown-gold translates to 10 ×10 ±5%, or 100 Ω ±5%.
Red-black-brown-gold translates to 20 ×10 ±5%, or 200 Ω ±5%.
Next, we'll draw each circuit, find the total or equivalent resistance, then use Ohm's law to find currents.
Series
Wiring the resistors in series, the total resistance is:
R = 100 Ω + 100 Ω + 200 Ω
R = 400 Ω
Resistors in series have the same current. The current passing through the battery, and through the resistors, can be found with Ohm's law.
V = IR
6 V = I (400 Ω)
I = 0.015 A
I = 15 mA
Parallel
Wiring the resistors in parallel, the total resistance is:
1/R = 1 / 100 Ω + 1 / 100 Ω + 1 / 200 Ω
1/R = 5 / 200 Ω
R = 40 Ω
Resistors in parallel have the same voltage. Using Ohm's law, the current through each resistor is:
I = V / R
I = 6 V / 100 Ω = 0.06 A = 60 mA
I = 6 V / 100 Ω = 0.06 A = 60 mA
I = 6 V / 200 Ω = 0.03 A = 30 mA
The current through the battery is:
I = 6 V / 40 Ω = 0.15 A = 150 mA
Combination
If the current is 60 mA, then the total resistance must be:
R = V / I
R = 6 V / 0.06 A
R = 100 Ω
The total resistance is not greater than any of the individual resistors, so the battery is not directly in series with any of the resistors. That leaves two options: both 100 Ω resistors in series with each other and in parallel with the 200 Ω resistor, or one 100 Ω resistor in series with the 200 Ω resistor and in parallel with the other 100 Ω resistor.
The total resistance of the first combination is:
1 / R = 1 / (100 Ω + 100 Ω) + 1 / 200 Ω
R = 100 Ω
The total resistance of the second combination is:
1 / R = 1 / (100 Ω + 200 Ω) + 1 / 100 Ω
R = 75 Ω
Therefore, it must be the first combination.
