# a)Derive an expression for the equivalent resistance of three reistors joined in (a)series (b)parallelb)Derive an expression for electrical energy and electrical power.

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a)if two resistors are in parallel the voltage across them is same
therefore
V=I*R (R=Equivalent resistance)
V=I1*R1
I1=V/R1

V=I2*R2
I2=V/R2

I=I1+I2
V/R=V/R1+V/R2
=> 1/R=1/R1+1/R2

If two resistors in series then current is same in both resistors.
V1=I*R1
V2=I*R2

V=V1+V2
I*R=I*R1+I*R2
R=R1+R2

b)If a current of 'I' amperes flows through a conductor of resistance 'R' ohm for a time 't' seconds when the potential difference across its ends is 'V' volt, then the electric power consumed

P=

P=

Using Ohm's law, 'Power' can also be expressed as

P=I2R

Or P=

The unit of power is 'watt'.

c) electric energy is simply = power * time taken ..

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Series combination

In a series connection, all resistors are connected end to end (lengthwise) with each other. In such connections, the total resistance of the circuit increases. The given figure shows three resistors of resistance R1, R2, and R3 respectively connected in a series with each other.

The equivalent resistance of the resistors connected in series is given by the algebraic sum of their individual resistances.

Equivalent resistance or RS = R1 + R2 + R3

derivation of it :

Suppose, there are ‘n’ resistances connected in series. The resistances are: R 1 , R 2 , R 3 , R 4 …… R n . Voltage ‘V’ is applied across the ends of the connection. Let I current flown through the series of resistances.

Since, current I will be same through all the resistances and the sum of voltage drop across all the resistances gives us the voltage ‘V’. Therefore,

V = IR 1 + IR 2 + IR 3 + IR 4 +………….. IR n

=> V = I(R 1 + R 2 + R 3 + R 4 +………….. R n )

Thus, the series of resistances can be summed up and the equivalent resistance of the circuit is the sum of the resistances.

Therefore, V = IR s

Where, R s = R 1 + R 2 + R 3 + R 4 +………….. R n

Parallel combination

Here three resistances are connected in parallel.In this case the potential difference across the ends of all the resistances will be same and it will be equal to the voltage of the battery used.

Suppose the total current flowing through the circuit=I,then the current passing through resistance

Current through and current through

power :

Electrical Energy is E = P × t

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