Question

A 6 ohm, 5 ohm, and 8 ohm resistor are connected in series with a 30 V battery. What is the total
resistance and the current through the 8 ohm resistor?

answers below:
Total Resistance = 19 ohms. Current = 0.63 A.

Total Resistance = 2.03 ohms. Current = 14.75 A.

Total Resistance = 2.03 ohms. Current = 1.58 A.

Total Resistance = 19 ohms. Current = 1.58 A.

Answer 1

To find the total resistance in a series circuit, you simply add the individual resistances together.

Given resistances:
- R1 = 6 ohms
- R2 = 5 ohms
- R3 = 8 ohms

Total Resistance (R_total) = R1 + R2 + R3
R_total = 6 ohms + 5 ohms + 8 ohms = 19 ohms

Next, to find the current through the 8 ohm resistor, we use Ohm's Law:

\( V = I \times R \)

Where:
- V = voltage (30 V)
- I = current (what we want to find)
- R = total resistance (19 ohms)

Rearranging Ohm's Law to find the current:

\( I = \frac{V}{R} \)

Substituting in the values:

\( I = \frac{30 V}{19 \text{ ohms}} \)

Calculating this gives:

\( I \approx 1.58 \text{ A} \)

Thus, the total resistance is 19 ohms and the current through the 8 ohm resistor is 1.58 A.

The correct answer is:
**Total Resistance = 19 ohms. Current = 1.58 A.**