Question

The four resistors in the given circuit has the values 5 ohms , 6 ohms ,2 ohms, 4 ohms respectively.the value of v is 10 v.the net resistance and current in the circuit are

Answer 1

Correct Question :

Four resistances of 5Ω, 6Ω, 2Ω and 4Ω are connected in series across a battery of 10V. Find the net resistance and current in the circuit.

Solution :

❒ Equivalent resistance of circuit :

Equivalent resistance of series connection is given by

• R = R₁ + R₂ + ... + Rₙ

By substituting the given values;

➠ R = R₁ + R₂ + R₃ + R₄

➠ R = 5 + 6 + 2 + 4

➠ R = 17 Ω .......... (I)

❒ Current flow in the circuit :

As per ohm's law, current flow in the circuit is directly proportional to the applied potential difference$.$

Mathematically, V = I × R

• V denotes applied voltage
• I denotes current
• R denotes resistance

➠ V = I × R

➠ 10 = I × 17

➠ I = 10/17

➠ I = 0.59 A .......... (II)

Answer 2

★ Provided Question ★

The four resistors in the given circuit has the values 5 ohms , 6 ohms ,2 ohms, 4 ohms respectively.the value of v is 10 V .The net resistance and current in the circuit are?

★ Required Solution ★

Let's assume,

• 5Ω resistor as $\bf { R_1}$
• 6Ω resistor as $\bf { R_2}$
• 2Ω resistor as $\bf { R_3}$
• 4Ω resistor as $\bf { R_4}$

As per the provided question we are given that the resistors are connected in series combination.So we'll apply here the given formula :–

• ${\boxed {\huge {\bf {\pink { R_s = R_1 + R_2 + R_3............}}}}}$

Substitute the values:–

$\rm {:\implies R_s = R_1 + R_2 + R_3 + R_4 }$

⠀⠀⠀⠀⠀⠀

$\rm {:\implies R_s = 5Ω + 6Ω + 2Ω +4Ω }$

⠀⠀⠀⠀⠀⠀

$\rm \red {:\implies R_s = 17Ω }$

Therefore, the net resistance is 17Ω.

Now, we'll find the current by the ohm' law:

We know that,

• ${\boxed {\huge {\bf {\pink { V = IR}}}}}$

Therefore,

• ${\boxed {\huge {\bf {\pink { I = \dfrac{V}{R} }}}}}$

Where,

• V(Potential difference) = 10V

• I (current) = ?⠀⠀⠀⠀⠀⠀ [To calculate]

• R ( Resistance) = 17Ω

Substitute the values:

$\rm {:\implies I = \dfrac{10}{17} }$

⠀⠀⠀⠀⠀⠀

$\rm \red{:\implies I = 0.59A}$

____________________________

More Information:

• The property of a conductor due to which it opposes the flow of current through it is called resistance.

• The resistance of a conductor depends on the length thickness temperature and nature of the material of the conductor.

• The SI unit of resistance is ohm (Ω).

The resistance can be into combination:

✤ Series Combination:

The sum of individual resistances is equal to the total resistance in the series combination.

Formula:${\boxed {\large {\bf {\purple { R_s = R_1 + R_2 + R_3..........}}}}}$

✤ Parallel Combination:

The sum of reciprocals of all the individual resistances is equal to the reciprocal of the total resistance in the parallel combination.

Formula: ${\boxed {\large {\bf {\purple { \dfrac{1}{R_p} = \dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3} ..........}}}}}$

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