Question

A resistor with an unknown resistance is connected in parallel to a 13 Ω resistor. When both resistors are connected in parallel to an emf source of 23 V, the current through the unknown resistor is measured with an ammeter to be 4 A. What is the resistance of the unknown resistor? Answer in units of Ω.

Answer 1

Answer:

R2 = 10.31Ω

Explanation:

For two resistors in parallel you have that the equivalent resistance is:

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$      (1)

R1 =  13 Ω

R2 = ?

The equivalent resistance of the circuit can also be calculated by using the Ohm's law:

$I=\frac{V}{R_{eq}}\\\\R_{eq}=\frac{V}{I}$            (2)

V: emf source voltage = 23 V

I: current = 4 A

You calculate the Req by using the equation (2):

$R_{eq}=\frac{23V}{4A}=5.75\Omega$

Now, you can calculate the unknown resistor R2 by using the equation (1):

$\frac{1}{R_2}=\frac{1}{R_{eq}}-\frac{1}{R_1}\\\\R_2=\frac{R_{eq}R_1}{R_1-R_{eq}}\\\\R_2=\frac{(5.75\Omega)(13\Omega)}{13\Omega-5.75\Omega}=10.31\Omega$

hence, the resistance of the unknown resistor is 10.31Ω

Answer 2

Answer:

The resistance of the unknown resistor is 5.75 Ω

Explanation:

We have a circuit containing two resistors connected in parallel.

One resistor is 13 Ω and the other resistor's resistance is unknown.

Both resistors are connected in parallel to an emf source of 23 V.

The current through the unknown resistor is measured with an ammeter to be 4 A.

Recall that in a parallel circuit the voltage across resistors remains the same but the current flowing through them is different.

So it means that the voltage across the unknown resistor is 23 V.

Since we already know the current flowing through the unknown resistor then using the Ohm's law

$V = IR \\\\R = V/I \\\\R = 23/4 \\\\R = 5.75 \: \Omega$

Therefore, the resistance of the unknown resistor is 5.75 Ω