Question

a circuit diagram in which the resistors in parallel are 2 ohm,5 ohm,and 10 ohm with a battery of 10V. find a)the current through each resistors b)total current in the circuit and c)total resistance in the circuit

Answer 1

The diagram of the circuit is attached along with the answer. So, let's start with the problem!

We are given three resistors of resistances 2 ohms, 5 ohms and 10 ohms respectively connected in parallel and a battery with a potential difference of 10V.

As per the question, we need to find :-

(i) the current though each resistor

(ii) the total current in the circuit

(iii) the total Resistance in the circuit

So, let's come to thd first case!

(i) CURRENT THROUGH EACH RESISTOR

We know that,

Current through a circuit = The potential difference / The Resistance of the conductor

So,

I¹ = V/R¹
= 10/2
= 5 A

I² = V/R²
= 10/5
= 2 A

I³ = V/R³
= 10/10
= 1 A

(ii) TOTAL CURRENT IN THE CIRCUIT

In this part too, we will have to use the same formula. The only difference will be, we will put the value of the Equivalent Resistance in the formula instead of Individual Resistance as we have used in the previous part. Thus is because we need to find the Total Current flowing through the circuit.

The Equivalent Resistance will be (parallel combination)

$\frac{1}{r} = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} \\ \\ \frac{1}{r} = \frac{5 + 2 + 1}{10} \\ \\ \frac{1}{r} = \frac{8}{10} \\ \\ r = \frac{5}{4} = 1.25 \: ohm$

I = V/Rε
= 10/1.25
= 8 A

(iii) TOTAL RESISTANCE IN THE CIRCUIT

Coming to thd total Resistance in the circuit, we have already calculated it above. Because, the resistors are put in parallel combination, we have used the reciprocal formula.

$\frac{1}{r} = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} \\ \\ \frac{1}{r} = \frac{5 + 2 + 1}{10} \\ \\ \frac{1}{r} = \frac{8}{10} \\ \\ r = \frac{5}{4} = 1.25 \:ohm$