the total resistance in a circuit with two parallel resistors is 2 ohms and ( r_1 ) is 6 ohms. using the…
the total resistance in a circuit with two parallel resistors is 2 ohms and ( r_1 ) is 6 ohms. using the equation for ( r_2 ), in terms of ( r_t ) and ( r_1 ), what is ( r_2 )? ( r_2 ) is (square) ohms.
Answer
Explanation:
Step1: Recall parallel resistance formula
The formula for total resistance ( R_T ) of two parallel resistors ( R_1 ) and ( R_2 ) is ( \frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2} ). We need to solve for ( R_2 ).
Step2: Rearrange the formula to solve for ( R_2 )
First, subtract ( \frac{1}{R_1} ) from both sides: ( \frac{1}{R_2}=\frac{1}{R_T}-\frac{1}{R_1} ). Then find a common denominator: ( \frac{1}{R_2}=\frac{R_1 - R_T}{R_T R_1} ). Taking the reciprocal of both sides gives ( R_2=\frac{R_T R_1}{R_1 - R_T} ).
Step3: Substitute the given values
We know ( R_T = 2 ) ohms and ( R_1 = 6 ) ohms. Substitute these into the formula: ( R_2=\frac{2\times6}{6 - 2}=\frac{12}{4}=3 ).
Answer:
3