Combination of Resistors — Series and Parallel MCQ Quiz - Objective Question with Answer for Combination of Resistors — Series and Parallel - Download Free PDF

Correct option is: (2) 2.0 A

R_AB = (1Ω / 3Ω) in series with (2Ω / 4Ω)

⇒ (1 × 3) / (1 + 3) + (2 × 4) / (2 + 4)

= 3 / 4 + 8 / 6 = (9 + 16) / 12 = 25 / 12 Ω

Now total current through the cell

I = 50 / (25 / 12) = 24 A

I_1Ω = (3 / 4) × 24 = 18 A, I_3Ω = (1 / 4) × 24 = 6 A

I_2Ω = (4 / 6) × 24 = 16 A, I_4Ω = (2 / 6) × 24 = 8 A

Using junction rule at C,

I_CD = 18 − 16 = 2 A (from C to D)

Correct option is: (3) R / 16

After being cut into 8 equal pieces,

⇒ Resistance of each piece = R′ = R / 8

Each set has 4 pieces in parallel combination

1 / R'' = 8 / R + 8 / R + 8 / R + 8 / R 

⇒ Resistance of each set = R″ = R / 32

Both sets are connected in series

∴ R_eq = R″ + R″ = 2 × (R / 32) = R / 16

Calculation:

The loop ABCDEF will be similar to balance wheatstone bridge as 

5/3 = 2.5/1.5

Thus the circuit will be:

Thus the equivalent circuit will be 

The total resistance is R = 8/3 +1/3 +1.5 + 5.5 = 10 Ω  

The total current will be 

I = V/ R = 5 / 10 = 1/2 A.

Calculation: 

Initially 5 Ω and 5 Ω are in series and then in parallel with 10 Ω this pattern continues thus

Rnet = 5 Ω

∴  The equivalent resistance is 5 Ω

Calculation:
Node P and Q are equipotential and node S and T are equipotential due to the formation of a Wheatstone bridge across them. Thus, no current passes through PQ and ST.

Now, for the current calculations:
I₁ = 12 / 4 = 3 A
I₂ = I₁ (12 / (6 + 12)) = 2 A

Now, point P and Q are equipotential, and point S and T are equipotential. From the resistor PS, current flows from P to S, hence the voltage at point P is higher than the voltage at point S. Since P is equipotential with Q, Q also has a higher potential than S.

CONCEPT:

• Resistance is the ability of any electrical component to resist electric current across it.
• Equivalent Resistance can be defined as the resistance of the resistor which will replace all the resistors between two points and will draw the same current between these two points as it was flowing Earlier.
• Ohms Law: At constant temperature, a potential difference is the product of current and resistance.

Series and Parallel Connection:

CALCULATION:

In the given diagram, the three 3Ω resistors are in parallel with each other.

The Equivalent resistance across them R' can be represented as 

\(\frac {1}{R'} = \frac{1}{3 Ω} + \frac{1}{3 Ω} + \frac{1}{3 Ω} \)

\(\implies \frac {1}{R'} = \frac{3}{3 Ω}\)

\(\implies R' = \frac{3 Ω }{3}\)

⇒ R' = 1Ω 

Now, this combination is in series with a 4Ω resistor.

So, Equivalent resistance

R = R' + 4Ω = 1Ω + 4Ω = 5Ω

So, 5Ω is the correct option.

CONCEPT:

• Resistance: The measurement of the opposition of the flow of electric current through a conductor is called the resistance of that conductor. It is denoted by R.

There are mainly two ways of the combination of resistances:

• Resistances in series combination: When two or more resistances are connected one after another such that the same current flows through them are called resistances in series.

The net resistance/equivalent resistance (R) of resistances in series is given by:

Equivalent resistance, R = R1 + R2

• Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

• Ohm’s law: At constant temperature and other physical quantities, the potential difference across a current-carrying wire is directly proportional to the current flowing through it.

V= R I

Where V is the potential difference, R is resistance and I is current.

CALCULATION:

Given that:

Resistance of Motor (R₁) = 90 ohm       

Resistance of a bulb (R₂) = 60 ohm       

Resistance of a Fan (R₃) = 30 ohm       

Potential difference (V) = 240 volt       

Total resistance of the three appliances in parallel:

1/R = 1/R1 + 1/R2 + 1/R3 = 1/90 + 1/60 + 1/30            

⇒ 1/R = 11 / 180  

So R = 16.36 Ohm

As we know that,

Ohm's Law, V = I x R

⇒ I = V/R 

⇒ Electric current (I) = 240 / 16.36 = 14.66 A ~ 15 A.

So option 1 is correct.

Concept:

Resistance:

• Resistance is the property of the substance to resist the flow of electric current through it.
• In the conductor, Resistance, \(R=ρ\frac{l}{A}\), where, ρ = resistivity, l = length, A = cross-sectional area

There are two types of combinations of resistance. 

• Series combination- In this type of combination, resistors are usually connected in a sequential manner one after another. The current through each resistor is the same.
  • R_eq = R₁ + R₂ + R₃ + - - -

• Parallel- In this type of connection, the resistors are usually connected on parallel wires originating from a common point. In this case, the voltage through each resistor is the same.
  • \(\frac {1}{R_{eq}}=\frac 1{R_1}+\frac 1{R_2}+\frac 1{R_3} +--\)+....

Calculation:

Calculation:

Given,

Resistance of the original wire, R = R

The wire is divided into m equal parts. Resistance of each part,

\(R_{\text{part}} = \frac{R}{m}\)

All m parts are connected in parallel. The effective resistance for parallel combination is given by,

\(\frac{1}{R_{\text{eq}}} = \frac{1}{R_{\text{part}}} + \frac{1}{R_{\text{part}}} + \ldots + m \text{ terms}\)

\(\frac{1}{R_{\text{eq}}} = m \times \frac{1}{\left(\frac{R}{m}\right)} = \frac{m^2}{R}\)

Hence, the effective resistance is:

\(R_{\text{eq}} = \frac{R}{m^2}\)

∴ The effective resistance of the combination is \(R_{\text{eq}} = \frac{R}{m^2}\).

CONCEPT:

• Ohm’s law: At constant temperature and other physical quantities, the potential difference across a current-carrying wire is directly proportional to the current flowing through it.

V = RI

Where V is the potential difference, R is resistance and I is current.

• Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

Given that:

Potential (V) = 12 V

R₁ = 80 Ω, R₂ = 120 Ω and R₃ = 240 Ω 

So equivalent resistance (R) =?

 1/R = 1/R₁ + 1/R₂ + 1/R₃ = 1/80 + 1/120 + 1/240 = 6/240 = 1/40

R = 40 Ω 

According to Ohm’s law 

⇒ I = V/R

Electric current drawn (I) = 12/40 = 0.3 A

So option 1 is correct.

CONCEPT:

• Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

Given that,

R₁ = \(R\ Ω\)

R₂ = \(20\ Ω\)

Net resistance/effective resistance (R) = 15 Ω 

Use the above-given formula for the parallel combination:

\({{1\over 15}={{1\over R}+{1\over 20}}}\)

\(20R= 300+15R\)

\(5R=300\)

∴\(R=60\ Ω.\)

CONCEPT:

• Resistance: The obstruction offered to the flow of current is known as the resistance. It is denoted by R.
• When two or more resistances are connected one after another such that the same current flows through them then it is called resistances in series.
• The equivalent resistance in series combination is will be

R_ser = R₁ + R₂ + R₃

• When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal then it is called resistances in parallel.

• The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

EXPLANATION:

Given that,

R₁ = R₂ = R₃ = R

When resistor are connected in series, then the equivalent resistance is

R_ser = R₁ + R₂ + R₃ = R + R + R = 3R       ---(1)

When the resistor is connected in parallel, then the equivalent resistance is

\(\frac{1}{{{R_{para}}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_2}}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R}\)

∴ R_para = R/3       ---(2)

Divide equation 1 and 2, we get

\(\frac{{{R_{ser}}}}{{{R_{para}}}} = \frac{{3R}}{{\frac{R}{3}}} = 9:1\)

CONCEPT:

• Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.
  • A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together.

​

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

Given that: R₁ = R₂ = 2 Ω 

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

\(\frac{1}{R} = \frac{1}{{{2}}} + \frac{1}{{{2}}} = 2/2 = 1\)

So Resultant resistance (R) = 1 Ω 

• The resultant resistance if two 2 Ω resistors are connected in parallel is 1 Ω. So option 2 is correct.

EXTRA POINTS:

• Resistances in series combination: When two or more resistances are connected one after another such that the same current flows through them are called as resistances in series.

The net resistance/equivalent resistance (R) of resistances in series is given by:

Equivalent resistance, R = R1 + R2

CONCEPT:

Resistance: The obstruction offered to the flow of current is known as the resistance. It is denoted by R.

• When two or more resistances are connected one after another such that the same current flows through them then it is called resistances in series.

The equivalent resistance in series combination is will be

R_ser = R₁ + R₂ 

When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal then it is called resistances in parallel.

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

In the above figure, 6Ω and 6Ω are connected in parallel.

The net resistance/equivalent resistance(R) of two 6Ω resistances connected in parallel is given by:

\(\frac{1}{{R'}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

\(\Rightarrow \frac{1}{{R'}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\)

R’ = 3 Ω

Now R’ and 3 Ω are in series,

∴ R_net = R’ + 3 Ω

⇒ R_net = 3 Ω + 3 Ω = 6 Ω

CONCEPT:

• Resistances in series combination: When two or more resistances are connected one after another such that the same current flows through them are called as resistances in series.

• The net resistance/equivalent resistance (R) of resistances in series is given by:
• Equivalent resistance, 

​R = R1 + R2      ...(1)

CALCULATION:

Given that: R₁ = 3 Ω  and R₂ = 6 Ω 

Using equation 1,

⇒ R = 3 + 6 = 9 Ω 

EXTRA POINTS:

• Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.

• The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

• Equivalent resistance decreases in the case of a parallel combination.
• In series combinations, the current remains constant while in case of parallel combination, the potential difference remains constant.

CONCEPT:

Resistance:

The measurement of the opposition of the flow of electric current through a conductor is called resistance of that conductor. It is denoted by R.

There are mainly two ways of the combination of resistances:

Resistances in series:

• When two or more resistances are connected one after another such that the same current flows through them are called as resistances in series.
• The net resistance/equivalent resistance (R) of resistances in series is given by:
• Equivalent resistance, 

​⇒ R = R1 + R2

Resistances in parallel:

• When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.
• The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(​⇒ \frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

• In parallel combination,

\(⇒ \frac{1}{R_{para}}= \frac{1}{4} + \frac{1}{4} =\frac{2}{4}=\frac{1}{2} \)

⇒ R_para = 2 Ω 

According to ohms law,

⇒ V = IR

• The current in the circuit is 

\(⇒ I = \frac{V}{R_{para}}=\frac{2}{2}=1\, A\)

• Let I is current in 4 Ω (above).

Current in 4 Ω (lower) = (1 - I)

Potential difference across 4 Ω (above) = Potential difference across 4 Ω (lower) 

⇒ 4 × I = 4 × (1 - I)   

⇒ 4I = 4 - 4I

⇒ 8I = 4

⇒ I = 4/8 = 0.5 A

• Hence across both resistors = I = 0.5 A