Question

Sally Sizzle builds a circuit by connecting three resistors in parallel with a 9V battery. The current in this circuit is 3.6 amps. Sally wants to add another resistor in parallel to increase the current to 4.6 amps. What should the resistance of this new resistor be? A) 0.5 Ohms B) 5 Ohms C) 9 Ohms D) 10 Ohm

Answer 1

Then answer is C 9 ohms

Answer 2

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:

$R_T = \frac{V}{I}=\frac{9 V}{3.6 A}=2.5 \Omega$

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:

$\frac{1}{R_T'}=\frac{1}{R_T}+\frac{1}{R_{new}}$ (1)

where $R_{new}$ is the new resistor that should be added.

Again, we can calculate the new equivalent resistance by using Ohm's law:

$R_T' = \frac{V}{I}=\frac{9 V}{4.6 A}=1.96 \Omega$

And substituting this value into eq.(1), we find the value of $R_{new}$:

$\frac{1}{R_{new}}=\frac{1}{R_T'}-\frac{1}{R_T}=\frac{1}{1.96 \Omega}-\frac{1}{2.5 \Omega}=0.110 \Omega^{-1}\\R_{new}=\frac{1}{0.110}=9 \Omega$