Calculate the total resistance of a parallel circuit with resistors: [tex]R_1=6 \Omega, R_2=3 \Omega[/tex].
Answer (1)
Use the formula for total resistance in a parallel circuit: R t o t a l 1 = R 1 1 + R 2 1 .
Substitute the given resistor values: R t o t a l 1 = 6 1 + 3 1 .
Simplify the equation: R t o t a l 1 = 2 1 .
Solve for R t o t a l : R t o t a l = 2Ω .
Explanation
Problem Analysis We are given two resistors, R 1 = 6Ω and R 2 = 3Ω , connected in parallel. Our goal is to find the total resistance of this parallel circuit.
Formula Introduction The formula for calculating the total resistance ( R t o t a l ) of resistors connected in parallel is given by: R t o t a l 1 = R 1 1 + R 2 1 We will use this formula to find the total resistance.
Substitution and Simplification Now, we substitute the given values of the resistors into the formula: R t o t a l 1 = 6 1 + 3 1 To add these fractions, we need a common denominator, which in this case is 6. So, we rewrite the equation as: R t o t a l 1 = 6 1 + 6 2 = 6 1 + 2 = 6 3 = 2 1
Finding Total Resistance Now we have: R t o t a l 1 = 2 1 To find R t o t a l , we take the reciprocal of both sides of the equation: R t o t a l = 2 1 1 = 2 Therefore, the total resistance of the parallel circuit is 2Ω .
Final Answer The total resistance of the parallel circuit with resistors R 1 = 6Ω and R 2 = 3Ω is 2Ω .
Examples
Imagine you are designing a simple electronic circuit for a DIY project, like a small lamp. You have two resistors with values 6 \Omega and 3 \Omega, and you need to connect them in parallel to achieve a specific resistance for the circuit to function correctly. Calculating the total resistance helps you determine if the combination of these resistors will provide the desired resistance value, ensuring your circuit works as intended. This calculation is crucial in electronics to control current and voltage levels in various components.
