Answer:
C) 9 Ohms
Explanation:
Initially, the voltage in the circuit is V = 9 V and the current is I = 3.6 A, with three resistors connected in parallel. We can calculate the initial equivalent resistance of the circuit by using Ohm's law:
[tex]R_T = \frac{V}{I}=\frac{9 V}{3.6 A}=2.5 \Omega[/tex]
Now Sally wants to add another resistor in parallel to increase the total current to I = 4.6 A. Since the new resistor is added in parallel, the new equivalent resistance will be:
[tex]\frac{1}{R_T'}=\frac{1}{R_T}+\frac{1}{R_{new}}[/tex] (1)
where [tex]R_{new}[/tex] is the new resistor that should be added.
Again, we can calculate the new equivalent resistance by using Ohm's law:
[tex]R_T' = \frac{V}{I}=\frac{9 V}{4.6 A}=1.96 \Omega[/tex]
And substituting this value into eq.(1), we find the value of [tex]R_{new}[/tex]:
[tex]\frac{1}{R_{new}}=\frac{1}{R_T'}-\frac{1}{R_T}=\frac{1}{1.96 \Omega}-\frac{1}{2.5 \Omega}=0.110 \Omega^{-1}\\R_{new}=\frac{1}{0.110}=9 \Omega[/tex]
