Question

Three resistors 3 Ohm, 10 Ohm, and 15 Ohm are connected parallel to each other across a 6V battery. The total resistance and the total current in the circuit are respectively​

Answer 1

QUESTION:

Three resistors 3 Ohm, 10 Ohm, and 15 Ohm are connected parallel to each other across a 6V battery. The total resistance and the total current in the circuit are respectively.

ANSWER:

REFER THE ATTACHMENT FOR THE FIGURE:

FORMULA USED FOR RESISTANCE:

AS THEY ARE CONNECTED IN PARALLEL SO,

$\frac{1}{equivalent \: resistance} = \frac{1}{r1} + \frac{1}{r2} + \frac{1}{r3}$

FOR CURRENT:

$current = \frac{potential \: difference}{equivalent \: resistane}$

$i = \frac{v}{r}$

1/equivalent resistantce= (1/3+1/10+1/15)

1/equivalent resistantce=10+3+2 /30

1/equivalent resistantce= 15/30 ohm

equivalent resistantce= 30/15 ohm

equivalent resistantce= 2 ohm.

CURRENT= 6 V/2 OHM

CURRENT= 3 AMPERE.

FINAL ANSWER:

$\huge\mathbb\pink{CURRENT= 3 A ; RESISTANCE= 2 OHM}$

Answer 2

Given:

R1 = 3 Ω

R2 = 10 Ω

R3 = 15 Ω

V = 6 V

To Find:

The total resistance (R) and the total current (I) in the circuit.

Calculation:

- In parallel combination, the total resistance is given as:

1/R = (1/R1) + (1/R2) + (1/R3)

⇒ 1/R = (1/3) + (1/10) + (1/15)

⇒ 1/R = (10 + 3 + 2) / 30

⇒ 1/R = 15 / 30

⇒ R = 30 / 15

⇒ R = 2 Ω

- The total current is given as:

I = V / R

⇒ I = 6 / 2

⇒ I = 3 A

- So, the total resistance (R) is 2 Ω and the total current (I) is 3 A in the circuit.