Combination of Resistors in Series and Parallel: Formulas, Videos, Q&As

An important part of electric circuits is Resistors. When a resistor connects to a combination of series and parallel connection it forms more complex circuit networks. Regulation of the current level of a device is a resistor’s functionality. To know more about resistors in series or parallel, let’s explore the article further!

Introduction

Resistors are two-terminal devices. Therefore, voltage division, regulation of current in the device and adjusting signal level are the functionality of a resistor. Representation of a resistor is done through Ohm’s Law. R = $ \frac{V}{ I} $ Many types of resistors are available and some are the following:

Wire-wound resistor.
Semi-conductor resistor.
Flim resistor.
Carbon Composition resistor.

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Resistor in Series

In this kind of connection, resistors are in a sequential array of resistors to form an electronic circuit/ device. Resistors are connected is in a single line and hence common current flows in the circuit. The connection is in such a manner that the current flowing through the 1st register has to then flow further through the 2nd register and then through 3rd. Therefore, a common current is flowing in connection with a resistor in series. At all point in the circuit, the current amoung the resistors is same. For example, I₁= I₂= I₃= I_t = 2ma All the resistors in series that is R₁, R₂, R₃ have current I₁, I₂, I₃ respectively and the current of the circuit is I_t. As resistors are connected in series the sum of the individual resistor is equal to the total resistance of the circuit. Let R₁, R₂, R₃ be the resistors connected in series and R_t be the total resistance of the circuit. so the total resistance of the circuit that is 12Ω, is the sum of all individual resistors R1, R2, R3 having 6KΩ, 4KΩ, 2KΩ respectively.

This circuit of the resistors in series can also be represented by

Therefore, the total resistance can be calculated as R₁ + R₂ + R₃ = R_t furthermore, the total resistance of the above resistors in series is given by R_t = 6KΩ + 4KΩ + 2KΩ = 12KΩ

The Equation of Resistors in Series

Since the connection of resistor is in a series fashion that is in the sequential array or continuously one after other. The total resistance is equal to the resistance value of each resistor in the device/ circuit. R₁+R₂+R₃+R₄+………………….R_n=R_t where R is the resistance of the resistor and R_n represents the resistor number or the total resistance value.

Resistor in Parallel

In this kind of connection, the terminals of resistors are connected to the same terminal of the other resistor to form an electronic circuit/ device. Resistors are connected is in parallel fashion and hence common voltage drop in the circuit. Unlike, series connection, in parallel connection, current can have multiple paths to flow through the circuit, hence parallel connection is also current dividers. Common voltage drop is across the parallelly connected circuits/networks. At the terminals of the circuit, the voltage drop is always the same. For example V_R1=V_R2=V_R3=V_RT=14V The voltage across R1 is equal to the voltage across R2 and similarly, equal to R3 and hence the total voltage drop is equal to the voltage across the circuit. Reciprocal of individual resistance of each resistor and the sum of all the reciprocated resistance of resistor will us the total resistance of the circuit. $ \frac{1}{(R_t)} $ = $ \frac{1}{(R_1)} $ + $ \frac{1}{(R_2)} $ + $ \frac{1}{(R_3)} $ +………… $ \frac{1}{(R_n)} $ Resistors in parallel

Questions For You

Q1: When three identical resistances are connected to form a triangle the resultant resistance between any two corners is 30

Ω

.The value of each resistance is:

90 $Ω$ 54 $Ω$
15 $Ω$
45 $Ω$

Answer. 45

Ω

Ω

R_{A B} = \frac{2 R \times R}{3 R} = \frac{2 R}{3} = 30

RA B = 3 R/2=3* 30/2

$\Rightarrow R = 45 Ω$

Q2. Identify the changes in a circuit on adding a light bulb in parallel to the actual resistance of the circuit. It will:

decrease the total resistance
increase the total resistance
make the voltage lost in each light bulb different
make the current through each light bulb the same
not change the total current through the circuit

Answer. decrease the total resistance. For a parallel combination of two resistances,
1/R_eq=1/R₁+1/R₂⟹Req< min {R₁, the R₂}
A light bulb has its own resistance and hence the total resistance of the circuit decreases when it is connected in parallel to the actual resistance of the circuit.

Q3.The least resistance that one can have from six resistors of each 0.1 ohm resistance is:

0.167 $Ω$
0.00167 $Ω$
1.67 $Ω$

Answer. 1.67 $Ω$ . Least resistance is possible when all are in parallel.
$\Rightarrow R_{e q} = \frac{R}{6} = \frac{0.1}{6} = 0.0167 Ω$ $\Rightarrow R_{e q} = \frac{R}{6} = \frac{0.1}{6} = 0.0167 Ω$ $\Rightarrow R_{e q} = \frac{R}{6} = \frac{0.1}{6} = 0.0167 Ω$