# Combination of Resistances(or Resistors)

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### Combination of Resistances(or Resistors)

Resistors in Series:-

Above picture shows the combination of resistors in series.
V = V1 + V2 + V3
Applying the Ohm’s law to the entire circuit, we have   V = I R
V1 = I R1
V2 = I R2
and V3 = I R3
I R = I R1 + I R2 + I R3
Rs = R1 +R2 + R3
so, when resistors are connected in series the equivalent resistance is the sum of the individual resistors.

Resistors in Parallel:-

The above picture shows the combination of resistors in parallel.

Total current i.e. I = I1 + I2 + I3
By applying Ohm’s law to the parallel combination of resistors, we have I = V/Rp
On applying Ohm’s law to each resistor, we have I1 = V /R1; I2 = V /R2; and I3 = V /R3
we have     V/Rp = V/R1 + V/R2 + V/R3
or
1/Rp = 1/R1 + 1/R2 + 1/R3
so, we conclude that when resistors are connected in parallel, then the effective resistance is the sum

Problem – A 6 ohm resistance wire is doubled up by folding. Calculate the new resistance of the wire.

The new resistance of the doubled up wire is 1.5 Ohm.

we will now study about Electric Power and how electric appliances produces heat or how electricity produces heat.

1. In the circuit diagram given alongside, find : (i) total resistance of the circuit, (ii) total current flowing in the circuit, and (iii) the potential difference across R1

2. A 5 V battery is connected to two 30 ohm resistors which are joined together in series.

(a) Draw a circuit diagram to represent this. Add an arrow to indicate the direction of conventional current flow in the circuit.

(b) What is the effective resistance of the two resistors ?

(c) Calculate the current that flows from the battery.

(d) What is the p.d. across each resistor ?

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