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What is the total resistance of a parallel circuit with two branches, each having a resistance of 1000 Ω?

A. 500 Ω
B. 2000 Ω
C. 250 Ω
D. 1000 Ω


Sagot :

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