Question

Resisters given as R1, R2,R3 are connected in series to a battery.Draw the circuit diagram .Show the arrangement . and derive the expression for the the equivalent resistance .Find the equivalent resistance where R1= 10 Ohm, R2=20 ohm R3= 30ohm ,voltage 6 V and now also find the current.​

Answer 1

Given :-

• Resistance of 3 resisters are R1, R2, and R3
• Resisters are in series
• R1 = 10 Ω
• R2 = 20 Ω
• R3 = 30 Ω
• Battery is connected with voltage of 6V

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To find :-

• Circuit diagram and its arrangement
• Derivation of the expression
• Equivalent resistance
• Current flowing

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Solution :-

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a) Circuit diagram and its arrangement

For the circuit diagram and its arrangement kindly refer to the above attachment.

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b) Derivation of the expression :-

As we know,

$Voltage (V) = Current (C) \times Resistance (R)$

So,

$V = IR$

According to the circuit diagram,

$= > V1 = IR1 \\ = > V2 = IR2 \\ = > V3 = IR3$

$V = V1 + V2 + V3$

In place of V we can write IR.

So,

$= > IR = IR1 + IR2 + IR3 \\ = > IR = I(R1 + R2 + R3)$

By cancelling I both the sides,

$\boxed{\bf{\large{\ {{R= R1+R2+R3}}}}}$

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c) Equivalent resistance :-

$= > R1= 10 Ω \\ = > R2 = 20 Ω \\ = > R3 = 30 Ω$

We know

When resistors are connected in series, the total equivalent resistance will be the sum of given resistors.

So,

$= > Rs = R1+R2+R3 \\ = > 10+20+30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > 60 Ω \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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d) Current flowing through the circuit :-

We know that,

= > I = V / R

= > I = 6 / 60

= > I = 0.01 A

So, 0.01 A of current is flowing through the circuit.

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Answer 2

Answer:

Hope it's helpful to you...