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Step 1:I'll solve this step-by-step using the parallel resistance formula:
Step 2:: Recall the formula for parallel resistance
For resistors in parallel, the total resistance ($$R_{total}$$) is calculated using the formula:
\frac{1}{R_{total}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ... + \frac{1}{R_{n}}
Step 3:: Identify the given resistors
- Resistor 1: $$R_{1} = 12 \Omega
- Resistor 2: R_{2} = 12 \Omega
Step 4:: Apply the parallel resistance formula
\frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{12}
Step 5:: Simplify the equation
\frac{1}{R_{total}} = \frac{2}{12} = \frac{1}{6}
Step 6:: Solve for total resistance
R_{total} = \frac{1}{\frac{1}{6}} = 6 \Omega
Final Answer
The total resistance of two 12 -ohm resistors in parallel is 6 \Omega.
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