Class 10 science Solutions English Medium

Connecting resistors to a circuit: 

The current through a conductor depends upon its resistance and the potential difference across its ends.

There are two methods of joining the resistors together.

(i) Series: When two or more resistances are joined end to end so that same current flows through each of them. The resistors connecting in such manner is called resistors connected in series.

Resistors R₁, R₂ and R₃ and a bulb are connected in series

Total Equivalent Resistance in Series: 

When we connent resistors R₁, R₂ and R₃ in series, the current (I) flowing through the resistance in series will remain same in every part of the circuit, where as the potential difference (V) across each resistor will be diffrerent. 

The total potential difference across a combination of resistors inseries is equal to the sum of potential difference across the individual resistors.

Therefore,

V = V₁ + V₂ + V₃          -------------------- (i) 

When we apply Ohm's law

V = IR                           --------------------(ii) 

So for each part we get;

V₁ = I R₁     -------------- (iii) 
V₂ = I R₂     -------------- (iv) 
V₃ = I R₃     -------------- (v) 

Adding (iii) (iv) (v) 

V₁ + V₂ + V₃ = I R₁ + I R₂ + I R₃       

V = I (R₁ + R₂ + R₃ )                using equation (i) 

IR = I (R₁ + R₂ + R₃ )              using equation (ii) (V = IR )

which gives

R = R₁ + R₂ + R₃   

Here R is total equivalent resistance in series which is equal to sums of individual resistances, R1, R2, R3, and is thus greater than any individual resistance. 

(ii) Parallel: When two or more resistances are connected across two point so that each of them provides a seperate path for current, The resistors connecting in such manner is called resistors connected in parallel.

Resistors R₁, R₂ and R₃ are connected in parallel. 

Total Equivalent Resistance in parallel:

When we connect the resistors R₁, R₂ and R₃ in parallel, The current (I) following in each resistors will be difference but the potential difference (V) across the each resistors will be same. 

Therefore,

I = I₁ + I₂ + I₃        -------------- (i)  [current is difference in each resistor]

Let R_p be the equivalent resistance of the parallel combination of resistors.  

By applying Ohm’s law to the parallel combination of resistors.

On applying Ohm’s law to each resistor, we have

adding equation (iii) (iv) and (v) 

Effect on current when resistors are connected in series: 

Let, Two resistors R₁ and R₂ of 3 Ω and 5 Ω are connected in series to a 6 V battery. What will be toatal resistance of circuit and current through the circuit.

Total resistance in circuit

R =  R₁ + R₂ 

   = 3 Ω + 5 Ω​ 

   = 8 Ω 

Now calculating for Current;

I = V/R 

  = 6/8 

  = 0.75 A 

Effect on current when resistors are connected in parallel: 

Same divices connected in parallel then resulting total resistance (R) and current (I)

Now calculating for Current;

See these result in a table 

Battery: Connections of two or more than two cells is callled battery. 

Ohm's Law

Ohm's Law: the electric current flowing through a metallic wire is directly proportional to the potential difference V, across its ends provided its temperature remains the same. This is called Ohm’s law.

V ∝ I

V ∝ I.constant

V/I = constant 

      = R

  V = IR 

Resistance