To determine the total resistance of a parallel circuit with two branches, each having a resistance of 1000 ohms, follow these steps:
1. Recall the formula for calculating the total resistance [tex]\( R_{total} \)[/tex] in a parallel circuit.
[tex]\[
\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}
\][/tex]
Here, [tex]\( R_1 \)[/tex] and [tex]\( R_2 \)[/tex] are the resistances of the two branches.
2. Substitute the resistances of the branches into the formula.
[tex]\[
\frac{1}{R_{total}} = \frac{1}{1000} + \frac{1}{1000}
\][/tex]
3. Simplify the right-hand side of the equation:
[tex]\[
\frac{1}{R_{total}} = \frac{1}{1000} + \frac{1}{1000} = \frac{2}{1000} = \frac{1}{500}
\][/tex]
4. Take the reciprocal of the right-hand side to find the total resistance:
[tex]\[
R_{total} = \frac{1}{\frac{1}{500}} = 500
\][/tex]
Therefore, the total resistance in a parallel circuit with two branches, each having a resistance of 1000 ohms, is 500 ohms.
The correct answer is:
O 500
