Question

09. Three resistances of 10 ohms, 15 ohms and 30 ohms are
connected in parallel. The total resistance of the
combination is
(A) 5 ohm
(B) 10 ohm
(C) 15 ohm
(D) 55 ohm​

Answer 1

Given :

Three resistors are connected in parallel.

• R₁ = 10Ω
• R₂ = 15Ω
• R₃ = 30Ω

To find :

The total resistance of the combination

Solution :

The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. .i.e.,

${ \leadsto{ \bf{\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}}}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{1}{10} + \dfrac{1}{15} + \dfrac{1}{30}}}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{3 + 2 + 1}{30} }}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{6}{30} }}}$

${ \leadsto{ \sf{\dfrac{1}{R} = \dfrac{1}{5} }}}$

${ \leadsto{ \sf{R=5 \: \Omega}}}$

thus, the total resistance of the combination is 5Ω.

Hence, Option (a) 5Ω is correct.

Answer 2

Answer:

Question

Three resistances of 10 ohms, 15 ohms and 30 ohms are

connected in parallel. The total resistance of the

combination is

Given

Three resistors are connected in parallel combination...

$•R _{1} = 10 \: ohm \\ •R _{2} = 15ohm \\ •R_{3} = 30ohm$

To find

The total resistance of the combination is

Solution

☄️A circuit is said to be connected in parallel when the voltage is the same across the resistors.

☄️The following relation gives the total resistance of a parallel circuit.

$\large \bold{ \frac{1}{ R_{eq} } = \frac{1}{ R_{1} } + \frac{1}{ R_{2} } + \frac{1}{ R_{3} } + ..... + \frac{1}{ R_{n} } }$

Now substitute the values in the above formula:

$\large \bold{ \frac{1}{R_{eq} } = \frac{1}{ 10} + \frac{1}{ 15 } + \frac{1}{ 30 } }$

$\bold{ \frac{1}{R_{eq} } = \frac{3 + 2 + 1 }{ 30} } \\ \\ \large \bold{ \frac{1}{R_{eq} } = \frac{6}{ 30}} = \frac{1}{5} \\ \ \bold \purple{\R_{eq} } = 5ohm$

so correct is (A) 5 ohm.

------------------------------------------

MoRE information!!!

✏️A circuit is composed of conductors (wire), power source, load, resistor and switch.

✏️Resistors control the flow of the electric current in a circuit.

✏️A circuit is said to be connected in series when the same amount of current flows through the resistors.

✏️The following relation gives the total resistance of a series circuit:

$\large \bold{ R_{eq} = R_{1}+ R_{2} +..... + R_{n}}$

____________________