Question

draw the diagram showing the resistors on series . explain the changes in potential difference and electric current.aply ohms law write the equation​

Answer 1

The equivalent series resistance is drawn .

The circuit showing Ohm's Law is drawn   .

Explanation:

Given as :

A series connection resistor with supply voltage

Let The resistance be $R_1$  ohm , $R_2$  ohm

The supply voltage = V  volt

Let Voltage across resistance $R_1$  = $V_1$    volt

Let Voltage across resistance $R_2$  = $V_2$    volt

The current flow through the circuit = I amp

According to question

For series connection of resistance , The current flow through each resistor is same . But voltage across each resistor are difference.

Some result about series resistance are :

(i) When two or more resistor are connected in series then equivalent resistance of the combination is equal to the resistance of individual resistor .

i.e     $R_e_q$  = $R_1$  + $R_2$ +   .............................+  $R_n$

(ii) When two or more resistor are connected in series current flow through each resistor is same .

(iii) When two or more resistor are connected in series then voltage across  the combination ( i.e across battery ) is equal to the sum of voltage drop across individual resistor .

i.e       $V_e_q$  = $v_1$  + $v_2$ +   .............................+  $v_n$

Again

From Ohm's Law

Voltage drop across resistor is directly proportional to the current flowing through them .

i.e     Voltage ∝ Current

Or,               V ∝ I

Or,               V = R I

The proportionate constant is resistance .

From figure

The circuit drawn in figure showing the three resistor connected across supply voltage.

Now,

For series resistance

voltage across  the combination ( i.e across battery ) is equal to the sum of voltage drop across individual resistor .

Voltage drop across resistor $R_1$

$v_1$ = I $R_1$

Voltage drop across resistor $R_2$

$v_2$ = I $R_2$

Voltage drop across resistor $R_3$

$v_3$ = I $R_3$

So, As per property of series resistance

 V = $v_1$  + $v_2$ + $v_3$

i.e  V = I $R_1$  +  I $R_2$ + I $R_3$

Or,  V = I ( $R_1$  +  $R_2$  +  $R_3$ )

And equivalent resistance  

  $R_e_q$   =  $R_1$  +  $R_2$  +  $R_3$

∴  V = I $R_e_q$

Hence, The equivalent series resistance is drawn .

The circuit showing Ohm's Law is drawn   . Answer

Answer 2

Resistors connected in series:

The resistors connected in series is given in the image below.

Let the two resistors be R₁ and R₂ and the potential difference across each resistor is V₁ and V₂ but the current flowing is same.

Let the current flowing through resistors be I

Since, the resistors are connected in series, the equivalent resistance of the resistors is equal to sum of the individual resistance.

Req = R₁ + R₂

Thus, the potential difference across each resistor is:

Veq = V₁ + V₂ → (equation 1)

On applying Ohm's law, we get,

V = IR

On applying the formula in potential difference, we get,

IReq = IR₁ + IR₂

IReq = I(R₁ + R₂)

∴ Req = R₁ + R₂