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