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(A) with the Help of a Circuit Diagram, Obtain the Relation for the Equivalent Resistance of Two Resistances Connected in Parallel. (B) in the Circuit Diagram Shown Below, Find: (I) Total - CBSE Class 10 - Science

Question

(a) With the help of a circuit diagram, obtain the relation for the equivalent resistance of two resistances connected in parallel.
(b) In the circuit diagram shown below, find:

(i) Total resistance.
(ii) Current shown by the ammeter

Solution

Let the individual resistance of the two resistors be R1 and R2 and their combined resistance be R. Let the total current flowing in the circuit be I and strength of the battery be volts. Then, from Ohm's law, we have:
V = IR ... (1)
We know that when resistors are connected in parallel, the potential drop across each resistance is the same.
Therefore:
I  = I1 I2
I = V/R1 + V/R2
I = V/(1/R1 + 1/R2) ... (2)
From the equations (1) and (2) we have:
1/R = 1/R1 + 1/R2

As shown Resistance 2Ω and 3Ω are in senies

We know resistance in series arrangement can be obtained as R=R_1+R_2

R=2Ω+3Ω=5Ω

$\text{ Since this 5 \Omega is in parallel with another 5 \Omega resistance therefore total resistance can be obtained as }$

1/R=1/R_1+1/R_2   "Here"  R_1=5Ω R_2=5Ω

1/R=1/5+1/5

$\frac{1}{R} = \frac{2}{5}$
$R = 2 . 5 \Omega$
"Total resistance of combination = 2 . 5 \Omega}"

The current shown by the ammeter A, i.e. the current in the circuit can be calculated as:

I=V/R

I=4/2.5=1.6A

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Solution (A) with the Help of a Circuit Diagram, Obtain the Relation for the Equivalent Resistance of Two Resistances Connected in Parallel. (B) in the Circuit Diagram Shown Below, Find: (I) Total Concept: Electric Current and Circuit.
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