Question

9. If in figure, R1 = 1032, R2 = 4012, R3 = 30N, RA = 2012,
R5 = 6012, and a 12 V battery is connected to the
arrangement. Calculate
R
R,
HHHH!
R
к
Eramin
Law
R
a. the total resistance in the circuit, and
b. the total current flowing in the circuit.​

Answer 1

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If, in Fig. straight R subscript 1 space equals space 10 space ohms comma space space straight R subscript 2 space equals space 40 space ohms comma space space straight R subscript 3 space equals space 30 space ohms comma space straight R subscript 4 space equals 20 space ohms comma space straight R subscript 5 space equals space 60 space ohms and a 12 volt battery is connected to the arrangement, calculate (a) the total resistance and (b) the total current flowing in the circuit.

(a) Let R' be the equivalent resistance of R1 and R2.

Here, R1 = 10straight capital omega , R2 = 40straight capital omega and they are connected in parallel with each other.

So,

fraction numerator 1 over denominator straight R apostrophe end fraction space equals space 1 over straight R subscript 1 plus 1 over straight R subscript 2 space equals space 1 over 10 plus 1 over 40 space equals space 5 over 40 space equals space 1 over 8

therefore straight R apostrophe space equals space 8 space straight capital omega

Let, R'' be the equivalent resistance ofstraight R subscript 3 comma space straight R subscript 4 space and space straight R subscript 5 which are connected in parallel.

So, their combinational resistance is,

fraction numerator 1 over denominator straight R apostrophe apostrophe end fraction space equals space 1 over straight R subscript 3 plus 1 over straight R subscript 4 plus 1 over straight R subscript 5

space space space space space space space space space space equals space space 1 over 30 plus 1 over 20 plus 1 over 60

space space space space space space space space space equals space 6 over 60 space

space space space space space space space space space space equals 1 over 10

i.e., straight R apostrophe apostrophe space equals space 10 space straight capital omega

Therefore, Total resistance is given by straight R space equals space straight R apostrophe space plus space straight R apostrophe apostrophe space equals space 8 space plus space 10 space equals space 18 space straight capital omega. space

(b) Total current flowing in the circuit is,

straight I space equals space straight V over straight R space equals space fraction numerator 12 space straight V over denominator 18 space straight capital omega end fraction space equals space 0.67 space straight A.

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