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The total resistance in a circuit with two parallel resistors is 2 ohms, and [tex]R_1[/tex] is 6 ohms.

Using the equation for [tex]R_2[/tex], in terms of [tex]R_T[/tex] and [tex]R_1[/tex], what is [tex]R_2[/tex]?
[tex]R_2[/tex] is [tex]\square[/tex] ohms.



Answer :

GinnyAnswer
Sure, let's find the value of the second resistor, [tex]\( R_2 \)[/tex], given the total resistance [tex]\( R_T \)[/tex] and the first resistor [tex]\( R_1 \)[/tex]:

The formula for the total resistance [tex]\( R_T \)[/tex] in a parallel circuit with resistors [tex]\( R_1 \)[/tex] and [tex]\( R_2 \)[/tex] is:

[tex]\[ \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} \][/tex]

We are given the values:
- [tex]\( R_T = 2 \)[/tex] ohms
- [tex]\( R_1 = 6 \)[/tex] ohms

First, we calculate the reciprocal of the total resistance:

[tex]\[ \frac{1}{R_T} = \frac{1}{2} = 0.5 \][/tex]

Next, we find the reciprocal of [tex]\( R_1 \)[/tex]:

[tex]\[ \frac{1}{R_1} = \frac{1}{6} = 0.16666666666666666 \][/tex]

Using these values, we can solve for the reciprocal of [tex]\( R_2 \)[/tex]:

[tex]\[ \frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1} \][/tex]

Substituting the known values:

[tex]\[ \frac{1}{R_2} = 0.5 - 0.16666666666666666 = 0.33333333333333337 \][/tex]

To find [tex]\( R_2 \)[/tex], we take the reciprocal of [tex]\( \frac{1}{R_2} \)[/tex]:

[tex]\[ R_2 = \frac{1}{0.33333333333333337} = 2.9999999999999996 \][/tex]

Therefore, the value of [tex]\( R_2 \)[/tex] is:

[tex]\[ R_2 = 3 \text{ ohms} \][/tex]

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