To calculate the total resistance in a parallel circuit, we use the formula for total resistance \( R_t \) in parallel:
\[ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]
where \( R_1, R_2, \) and \( R_3 \) are the resistances of the individual resistors. In your case, we have:
- \( R_B = 10 , \Omega \)
- \( R_C = 20 , \Omega \)
- \( R_D = 50 , \Omega \)
Now let's plug in the values into the formula:
\[ \frac{1}{R_t} = \frac{1}{10} + \frac{1}{20} + \frac{1}{50} \]
Calculating each term:
- \( \frac{1}{10} = 0.1 \)
- \( \frac{1}{20} = 0.05 \)
- \( \frac{1}{50} = 0.02 \)
Now, add these values together:
\[ \frac{1}{R_t} = 0.1 + 0.05 + 0.02 = 0.17 \]
Next, take the reciprocal to find the total resistance \( R_t \):
\[ R_t = \frac{1}{0.17} \approx 5.8824 , \Omega \]
Rounding to the tenths place:
\[ R_t \approx 5.9 , \Omega \]
Therefore, the total resistance in the circuit is approximately 5.9 Ohms.