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Question : 20
Total: 27
(a) How will you infer with the help of an experiment that the same current flows through every part of a circuit containing three resistors in series connected to a battery?
(b) Consider the given circuit and find the current flowing in the circuit and potential difference across the15 Ω
(a) Three resistorsR 1 , R 2 R 3
(b) Calculate the equivalent resistance of the following network:
(b) Consider the given circuit and find the current flowing in the circuit and potential difference across the
OR
(a) Three resistors
(b) Calculate the equivalent resistance of the following network:
Solution:
(a) Let three resistors R 1 , R 2 R 3
(b) Given,
R 1 = 5 Ω , R 2 = 10 Ω , R 3 = 15 Ω , V = 30 V
Total resistance,R = R 1 + R 2 + R 3
[ ∵ 5 Ω , 10 Ω 15 Ω
= 5 + 10 + 15
= 30 Ω
Potential difference,V = 30 V
Current in the circuit,I =
From Ohm's law.
I =
=
= 1 A
∴ = 1 A
Potential difference across15 Ω = ℝ 3
= 1 A × 15 Ω
= 15 V
OR
(a) LetR 1 , R 2 R 3 R
I =
I 1 =
I 2 =
I 3 =
I = I 1 + I 2 + I 3
Putting the values ofI , I 1 , I 2 I 3
=
+
+
V (
) = V (
+
+
)
=
+
+
(b) LetR P
∴
=
+
=
=
=
R P = 10 Ω .
Now, equivalent circuit becomes.∵ 10 Ω 10 Ω
∴
= 10 Ω + 10 Ω
= 20 Ω
When key is closed, the current starts flowing through the circuit. Take the reading of ammeter. Now change the position of ammeter to anywhere in between the resistors and take its reading. We will observe that in both the cases reading of ammeter will be same showing same current flows through every part of the circuit above.
(b) Given,
Total resistance,
Potential difference,
Current in the circuit,
From Ohm's law.
Potential difference across
OR
(a) Let
From Ohm's law,
Putting the values of
(b) Let
Now, equivalent circuit becomes.
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