Question

A cell of internal resistant 2.0 ohm and electromotive force (e.m.f.) 1.5 V is connected to a resistor of resistance 3.0 ohm what is the potential difference across 3ohm resistor. .(a) 5 V (b) 1.2 V (c) 0.9 V (d) 0.6 V

Answer 1

Answer :

• The potential difference across 3 Ω resistor is 0.9 V.

Explanation :

Given :

• Internal resistance of the cell, r = 2 Ω
• Electromotive force (e.m.f) of the cell,ε = 1.5 V
• Resistance in the resistor, R = 3 Ω

To find :

• Potential difference across the 3 Ω resistor, V = ?

Knowledge required :

⠀⠀⠀⠀⠀⠀⠀⠀⠀● Formula for Electromotive force (e.m.f) :

⠀⠀⠀⠀⠀⠀⠀⠀⠀ε = l(R + r)

Where,

• ε = Electromotive force
• l = Current
• R = Load resistance
• r = Internal resistance

⠀⠀⠀⠀⠀⠀⠀⠀⠀● Ohm's law :

⠀⠀⠀⠀⠀⠀⠀⠀⠀V = IR

Where,

• V = Potential difference
• I = Current
• R = Resistance

[Note : In a series circuit, the current passing through each resistor is equivalent to each other]

Solution :

First let us find the current in the circuit :

Using the formula for e.m.f and by substituting the values in it, we get :

⠀⠀⠀=> ε = l(R + r)

⠀⠀⠀=> 1.5 = I(3 + 2)

⠀⠀⠀=> 1.5 = I × 5

⠀⠀⠀=> 1.5/5 = l

⠀⠀⠀=> 0.3 = I

⠀⠀⠀⠀⠀∴ l = 0.3 A

Hence the current in the circuit is 0.3 A.

Now,

Let's find out the potential difference in the 3 Ω resistor:

By using the ohm's law and Substituting the values in it, we get :

⠀⠀⠀=> V = IR

⠀⠀⠀=> V = 0.3 × 3

⠀⠀⠀=> V = 0.9

⠀⠀⠀⠀⠀∴ V = 0.9 V

Therefore,

• Potential difference across the 3 Ω resistor, V = 0.9 V.

Answer 2

Answer:

$\huge \bf \: required \: answer$

Firstly we will see the formula.

$\huge \sf \: e \: = i(R+ r)$

Here,

E = Electromagnetic force

I = Current

R = Load resistance

r = Internal Resistance

Now,

Ohm's law

$\huge \bf \: v \: = ir$

V = Potential difference

I = Current

R = Resistance

Now,

Let's solve

$\sf \implies \: e \: = i(R + r)$

$\sf \implies \: 1.5 = i(2 + 3)$

$\sf \implies \: 1.5 = 5 \times i$

$\sf \implies \: \frac{1.5}{5} = i$

$\sf \implies \: i \: = 0.3$

$\huge \fbox {current \: = 0.3 a}$

Let's find potential difference

We will apply Ohm's law

$\sf \implies \: v \: = i \times r$

$\sf \implies \: v \: = 0.3 \times 3$

$\sf \implies \: v \: = 0.9$

Therefore, potential difference across 3ohm resistor is 0.9 Volt