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Q.

A parallel combination of $3$ resistors take a net current of $7.5 A$ from a supply of $30 V$ . If $2$

resistors are $10 ohm$ and $12 ohm$ , then which of the following is the resistance of the third resistor?

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a

25 ohm

b

15 ohm

c

10 ohm

d

5 ohm

answer is B.

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Detailed Solution

The third resistor is given by

15 ohm

Two of the resistances are

12 ohm and 10 ohm

Three resistors take a current of

7.5 A

Current,

I = 30 V

To find the third one of the resistance,
A resistor is an acquiescent two-terminal electrical element that executes electrical resistance
as a circuit element. Resistors decrease the current flow and lower voltage levels within
circuits.
Most circuits usually have better additional than one resistor to determine the flow of charges
in a circuit. The two easiest combinations of resistors are – series and parallel.
Total current

= 7.5 A

V = 30 V

\frac{V}{I}

=

\frac{30}{7.5}

= 4

R_{total}

=

4 ohm

Let the third resistor be

R

Hence

\frac{1}{R}

=

\frac{1}{10}

+

\frac{1}{12}

+

\frac{1}{R}

\Rightarrow \frac{1}{4}

=

\frac{1}{10}

+

\frac{1}{12}

+

\frac{1}{R}

\Rightarrow \frac{1}{R}

=

\frac{1}{4}

+

\frac{1}{10}

+

\frac{1}{12}

\Rightarrow \frac{1}{R}

=

\frac{15 - 6 - 5}{60}

\Rightarrow \frac{1}{R}

=

\frac{4}{60}

\Rightarrow \frac{1}{R} = \frac{1}{15}

\Rightarrow R = 15 ohm

Hence, The third one is

R = 15 ohm

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