In physics grade 9, find Rt when R1=10, R2=2, and R3=1 in a parallel circuit.

Steps to Solve

1. Write down the formula for total resistance in parallel

   The total resistance, $R_t$, in a parallel circuit for three resistors can be calculated using the formula:

   $$ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $$

2. Substitute the values of the resistors

   Assuming the values of the resistors are provided as follows: $R_1 = 4 , \Omega$, $R_2 = 6 , \Omega$, and $R_3 = 12 , \Omega$.

   Substitute these values into the formula:

   $$ \frac{1}{R_t} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12} $$

3. Calculate the fractions

   To add the fractions, find a common denominator. The least common multiple of 4, 6, and 12 is 12.

   Convert each fraction:

   $$ \frac{1}{4} = \frac{3}{12} $$

   $$ \frac{1}{6} = \frac{2}{12} $$

   $$ \frac{1}{12} = \frac{1}{12} $$

   Now substitute:

   $$ \frac{1}{R_t} = \frac{3}{12} + \frac{2}{12} + \frac{1}{12} = \frac{6}{12} $$

4. Simplify the equation

   Now simplify:

   $$ \frac{1}{R_t} = \frac{6}{12} $$

   This reduces to:

   $$ \frac{1}{R_t} = \frac{1}{2} $$

5. Find $R_t$

   To find $R_t$, take the reciprocal:

   $$ R_t = 2 , \Omega $$