Answer
The current is 0.83 amps .
Option (C) is correct .
Explanation :
Formula for parallel resistors
\(\frac{1}{R_{Parallel}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}\)
As given
A combined circuit has two resistors in parallel (10.0 ohms and 14.0 ohms) .
\(R_{1}= 10\ ohms\)
\(R_{2}= 14\ ohms\)
Putting all the values in the above
\(\frac{1}{R_{Parallel}} = \frac{1}{10} + \frac{1}{14}\)
L.C.M of (10,14) = 70
\(\frac{1}{R_{Parallel}} = \frac{7+5}{70}\)
\(\frac{1}{R_{Parallel}} = \frac{12}{70}\)
\(R_{Parallel} = \frac{70}{12}\)
\(R_{Parallel} = 5.83\ ohms\ (Approx)\)
As given
Another resistors in the series is 5.0 ohms .
Formula
\(R_{Total}=R_{Parallel}+ R_{3}\)
\(R_{Parallel}=5.83\ ohms\)
\(R_{3}=5\ ohms\)
\(R_{Total}=5.83+5\)
\(R_{Total}=10.83\ ohms\)
Now by using the ohms law .
\(I = \frac{V}{R}\)
Where V is voltage , R is resistance and I is current .
As given
The power source is 9.0 volts .
V = 9 volts
\(R_{Total}=10.83\ ohms\)
Putting values in ohms law
\(I = \frac{9}{10.83}\)
I = 0.83 amps (Approx)
Therefore the current is 0.83 amps .
Option (C) is correct .
