Question

1. a 6ω and a 6ω resistor are in parallel. what is the equivalent resistance?

3ω
1ω
6ω
12ω

1. a 5ω and a 10ω resistor are in parallel. find the equivalent resistance.

0.09ω
3.33ω
10ω
15ω

1. what are the three basic types of circuits?
2. five resistors are in series. if each resistor is the same and has a resistance of 5ω, what is the equivalent resistance of the circuit?

1ω

Explanation:

Step1: Formula for parallel resistors

For two resistors \(R_1\) and \(R_2\) in parallel, the equivalent resistance \(R_{eq}\) is given by \(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\).

Step2: Solve for first problem

Given \(R_1 = 6\Omega\) and \(R_2=6\Omega\), then \(\frac{1}{R_{eq}}=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}\), so \(R_{eq} = 3\Omega\).

Step3: Solve for second problem

Given \(R_1 = 5\Omega\) and \(R_2 = 10\Omega\), \(\frac{1}{R_{eq}}=\frac{1}{5}+\frac{1}{10}=\frac{2 + 1}{10}=\frac{3}{10}\), so \(R_{eq}=\frac{10}{3}\approx3.33\Omega\).

Step4: Series resistors formula

For resistors in series \(R_{eq}=R_1+R_2+\cdots+R_n\). For five \(5\Omega\) resistors in series, \(R_{eq}=5\times5 = 25\Omega\) (but since this option is not in the first two questions' choices, focus on first two).

Answer:

1. \(3\Omega\) (first option)
2. \(3.33\Omega\) (second option)