What is the total resistance of a circuit containing a branch of three parallel 15-kiloohms resistors in series with a branch of two parallel resistors (1,000 ohms and 250 ohms)?

To find the total resistance in the described circuit, start by calculating the equivalent resistance of the three parallel 15-kiloohm resistors. The formula for calculating the equivalent resistance ( R_{eq} ) of resistors in parallel is:

[

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

]

Since all three resistors are 15 kiloohms, this becomes:

[

\frac{1}{R_{eq}} = \frac{1}{15000} + \frac{1}{15000} + \frac{1}{15000} = \frac{3}{15000}

]

Calculating the equivalent resistance results in:

[

R_{eq} = \frac{15000}{3} = 5000 \text{ ohms, or } 5 \text{ kiloohms}

]

Next, we need to find the equivalent resistance of the two parallel resistors of 1,000 ohms and 250 ohms:

[

\frac{1}{R_{eq2}} = \frac{1}{100