In various **electrical circuits**/gadgets, we often use resistors in various combinations.

There are basically two ways, in which resistors can be joined together. It can be either series combinations or parallel combination.

**Series Combination:**

This kind of combination in which the resistors are connected in series is called as Series combination.The positive terminal of one resistor is connected to negative terminal of another resistor.

Let’s apply Ohm’s law to the series combination, to find out the effective resistance of the circuit.

V = V_{1} + V_{2}+ V_{3}

V_{1}= IR_{1}, V_{2}= IR_{2}, V = IR_{3}

If all the three resistors are replaced by a single resistor, Req

And I is the current passing through the entire circuit,

IR_{eq}= IR_{1} + IR_{2} + IR_{3}

Req = R_{1}+ R_{2} + R_{3}

Same logic can be applied to circuit having more than 3 resistors,

R_{eq}= R_{1} +R_{2}+ R_{3}+———–R_{n}

Therefore we can conclude that in a series combination, the effective resistance is more than individual resistance.

**Parallel Combination:**

In the circuit, when resistors are connected in parallel across battery, we get parallel circuit

In the parallel combination, it’s observed that total current is equal to the sum of the separate currents through each branch of the combination.

I = I_{1}+ I_{2}

Let Rp be the effective resistance of parallel combination.

**Applying Ohm’s law,**

V/R_p = V/R_1 +V/R_2

1/R_p =1/R_1 +1/R_2

Same argument can be applied to more than 2 resistors also,

1/R_p =1/R_1 +1/R_2 +1/R_3 ±—-1/R_n

The total or effective resistance of a circuit having parallel combination is always lesser than smallest resistor.

**Advantages of parallel combination over series combination**

In the series circuit, the current is constant throughout the circuit. It would be unworkable to connect a gadget (like a geyser) which requires a higher value of current to a gadget (like (electric bulb) which requires lesser current in series.

The parallel combination works in above case as we can vary current through different branches.

Another major disadvantage is if one component breaks, the entire circuit breaks down.

**Multiple choice questions:**

**Q.1 the total resistance in parallel combination is**

**a)** Greater than individual resistor

**b)** Smaller than individual resistor

**c)** Same as each resistor

**Q.2 The total resistance of series combination is **

**a)** Greater than individual resistor

**b)** Smaller than individual resistor

**c)** Same as each resistor

**Q.3 Current is same throughout in**

**a)** Series circuit

**b)** Parallel circuit

**c)** Both of the above

**d)** None of the above

**Q.4 Voltage is same across each resistor in **

**a)** Parallel circuit

**b)** Series circuit

**c) **Both of the above

**d)** None of the above

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