cbse science physics electricity

1. Electricity
Class – 10
Aditya Mishra
Email: adityakumar2009@gmail.com
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2. RESISTANCE IN SERIES
R1 R2 R3
• Current through (I) the resistances is same
• Potential difference (V) across each resistor is different
I I
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3. 1 2 3
Total potential difference:
V = V + V + V
V = I R
1 1
V = I R
2 2
V = I R
3 3
V = I R
1 2 3
I R = I R + I R + I R
 
1 2 3
I R = I R + R + R
 
1 2 3
R = R + R + R
eq 1 2 3
R = R + R + R
------- (1)
------- (2)
------- (3)
------- (4)
------- (5)
Substituting equation 2,3,4 and 5 in equation 1
------- (6)
RESISTANCE IN SERIES
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4. eq
R = R + R + R
eq
R = 3R
eq
R = R + R + R + .......
eq
R = n R
---------------- (7)
---------------- (8)
• Equivalent resistance for three resistances each having a value of
R in series combination :
• Equivalent resistance for ‘n’ resistances each having a value of
R in series combination :
RESISTANCE IN SERIES
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5. RESISTANCE IN PARALLEL
• Potential difference ( V) across each resistance is same
• Current flowing ( I ) through each resistance is different
A R2
R3
R1
B
V
I1
I2
I3
I
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6. EQUIVALENT RESISTANCE FOR PARALLEL
COMBINATION
1 2 3
Total current (I ) = I + I + I
According to ohms law,
V= I R
 1
1
V
I =
R

2
2
V
I =
R

3
3
V
I =
R

1 2 3
I = I + I + I
1 2 3
V V V V
= + +
R R R R
1 2 3
V 1 1 1
= V + +
R R R R
 
 
 
eq 1 2 3
1 1 1 1
= + +
R R R R
(2)

(3)

(4)

Substituting eq. 2, 3, 4 in eq. 5
(6)

(1)

R2
R3
R1
A B
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7. PROBLEMS
eq 1 2 3
1 1 1 1
= + +
R R R R
eq 1 2
1 1 1
= +
R R R
2 1
eq 1 2 3
R +R
1 1
= +
R R R R
 
3 2 1 1 2
eq 1 2 3
R R +R R R
1
=
R R R R

3 2 3 1 1 2
eq 1 2 3
R R + R R R R
1
=
R R R R

1 2 3
eq
1 2 2 3 3 1
R R R
R =
R R + R R R R

eq
1 1 1 1 2
= + 2
R R R R R
 
 
 
 
1 2
eq
1 2
R R
R =
R + R
eq
1 1 1 1
= + ........
R R R R
n
 
   
 
eq
R
R
n

• For two resistances connected in parallel,
• For two resistances having same resistance
connected in parallel,
• For n resistances connected in parallel
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8. Q.1 Find the equivalent resistance for the parallel combination of
two resistor 5 ohm and 10 ohm?
1
R 5
 
eq
R ?

2
R 10
 
1 2
eq
1 2
R R
R
R +R

We know that for resistances
Connected in parallel ,
eq 1 2
1 1 1
R R R
 
 
 
eq
5 10
R
5 + 10


eq
50 10
R =
15 3
 
eq
R 3.33
 
Given:
To Find :
Solution :
Ans :
PROBLEMS
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9. Q.2 Three resistances of 2 ohm, 3 ohm and 5 ohm are connected
together. How the resistance should be connected to obtain
maximum resistance?
(a)
(b) (c)
Ans :
PROBLEMS
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10. 1
R = 2 Ω
2
R = 3 Ω
3
R = 5 Ω
R1 is parallel to R2
eq 1 2
1 1 1
= +
R R R
1 2
eq
1 2
R R
R =
R + R
eq
2 3
R =
2 + 3

eq
6
R =
5

3
R = 5 Ω
eq
6
R = Ω
5
(b)
eq1 eq 3
R = R + R
eq1
6
R = + 5
5
eq1
6 25
R =
5


eq1
31
R =
5

PROBLEMS
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