Find the total resistance of the network of the figure, where RA = 3 Ω, RB = 3 Ω, and RC = 6 Ω. Find the resistance RT.

Steps to Solve

1. Identify Resistor Arrangement

   In the given circuit, we can identify the resistors: RA = 3 Ω, RB = 3 Ω, and RC = 6 Ω. The two 3 Ω resistors (RA and RB) are in parallel, and the combination is in series with the 6 Ω resistor (RC).

2. Calculate Equivalent Resistance of RA and RB

   The formula for the equivalent resistance (R_parallel) of two resistors in parallel is given by:

   $$ \frac{1}{R_{parallel}} = \frac{1}{R_A} + \frac{1}{R_B} $$

   Substituting the values:

   $$ \frac{1}{R_{parallel}} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} $$

   Thus,

   $$ R_{parallel} = \frac{3}{2} = 1.5 , \Omega $$

3. Combine the Parallel Resistance with RC

   The total resistance (RT) is the sum of the equivalent resistance from the parallel combination (R_parallel) and the series resistor (RC):

   $$ R_T = R_{parallel} + R_C $$

   Substituting the values:

   $$ R_T = 1.5 + 6 = 7.5 , \Omega $$

4. Check for Error in Approach

   Since the options provided do not match our calculated total resistance of 7.5 Ω, let's re-evaluate the arrangement of the resistors to locate any oversight.

5. Final Check on Resistor Connections

   After careful evaluation, ensure that the understanding of resistors' arrangement is accurate, before confirming the calculations again or checking if any misinterpretation occurred.