Question

R1- 5 ohm
R2-20 ohm
R3-30 ohm

V=50v
Find total resistance
Total current
V(R1), I(R1)
V(R2), I(R2)
V(R3), I(R3)​

Answer 1

Given :

• R₁ = 5 ohms
• R₂ = 20 ohms
• R₃ = 30 ohms

Potential difference : 50 v

To find :

The total resistance and the total current.

Solution :

In the given figure R₂ and R₃ are connected in parallel combination.

We know that,

» The combined resistance of any number of resistance connected in series is equal to the sum of the individual resistances. i.e.,

R = R₁ + R₂

By substituting the values in the formula,

$\dashrightarrow \sf R_{23} = R_{2} + R_3$

$\dashrightarrow \sf R_{23} =20 + 30$

$\dashrightarrow \sf R_{23} = 50 \: ohms$

Now, R₂₃ and R₁ will be connected in parallel combination.

we know that,

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.,

1/R = 1/R₁ + 1/R₂

By substituting the values in the formula,

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{1}{R_{23}} + \dfrac{1}{ R_1}$

$\dashrightarrow \sf \dfrac{1}{R_{23}} = \dfrac{1}{50} + \dfrac{1}{5}$

$\dashrightarrow \sf \dfrac{1}{R_{23}} = \dfrac{1 + 10}{50}$

$\dashrightarrow \sf \dfrac{1}{R_{23}} = \dfrac{11}{50}$

$\dashrightarrow \sf R_{23} = \dfrac{50}{11}$

$\dashrightarrow \sf R_{23} = 4.54 \: ohms$

Thus, the total resistance is 4.54 ohms.

To find the current we can use ohm's law that is,

» At constant temperature the current flowing through a conductor is directly proportional to the potential difference across its ends.

Formula : V = RI

where,

• V denotes potential difference
• R denotes resistance
• I denotes current

substituting all the given values in the formula,

$\dashrightarrow \sf V = RI$

$\dashrightarrow \sf 50 = (4.54)I$

$\dashrightarrow \sf I = \dfrac{50}{4.54}$

$\dashrightarrow \sf I = 11.01 \: A$

Thus, the total current is 11.01 ampere.