Question

What is the equivalent resistance of the following circuit?

1 Ohms
10 Ohms
4 Ohms
6 Ohms

answers below:

1.52 Ohms

0.66 Ohms

0.91 Ohms

17 Ohms

Answer 1

To determine the equivalent resistance of the circuit with the given resistances (1 Ohm, 10 Ohm, 4 Ohm, and 6 Ohm), we need to know how these resistances are connected (in series, parallel, or a combination of both).

Assuming all four resistors are in series:
- The equivalent resistance \( R_{eq} \) is simply the sum of the resistances:
\[
R_{eq} = R_1 + R_2 + R_3 + R_4
\]
\[
R_{eq} = 1 \, \text{Ohm} + 10 \, \text{Ohm} + 4 \, \text{Ohm} + 6 \, \text{Ohm}
\]
\[
R_{eq} = 21 \, \text{Ohms}
\]

Assuming all four resistors are in parallel:
- The formula for equivalent resistance \( R_{eq} \) for parallel resistors is given by:
\[
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}
\]
\[
\frac{1}{R_{eq}} = \frac{1}{1} + \frac{1}{10} + \frac{1}{4} + \frac{1}{6}
\]
Calculating each term:
- \( \frac{1}{1} = 1 \)
- \( \frac{1}{10} = 0.1 \)
- \( \frac{1}{4} = 0.25 \)
- \( \frac{1}{6} \approx 0.1667 \)

Adding these:
\[
\frac{1}{R_{eq}} = 1 + 0.1 + 0.25 + 0.1667 \approx 1.5167
\]
Now, take the reciprocal:
\[
R_{eq} \approx \frac{1}{1.5167} \approx 0.6582 \, \text{Ohms}
\]

Since it seems likely these resistors are meant to be analyzed for parallel configuration, looking at the answer choices, \( 0.66 \, \text{Ohms} \) is the nearest and most appropriate.

Therefore, the equivalent resistance is approximately **0.66 Ohms**.