FACTORS AFFECTING RESISTANCE OF A CONDUCTOR

Remember the formula : R = ρ ɭ /A

where;  ‘ρ’ is resistivity, ‘ɭ’ is length and ‘A’ is cross sectional area of the conductor.

Explanation:

R ∝ ɭ ; meaning, resistance is directly proportional to length of the conductor. As length increases resistance of the conductor increases because electrons have to travel a longer distance in the conductor.
Analogy – Water takes more time to flow through a longer pipe.

R ∝ 1/A ; meaning, resistance is inversely proportional to cross section area of the conductor. As area increases resistance of the conductor decreases because electrons have a large area through which to flow through the conductor.
Analogy – Water take less time to flow through a pipe of larger diameter.

R ∝ ρ ; meaning, resistance is directly proportional to resistivity of the conductor. Resistivity is an intrinsic property of the material, As resistivity increases resistance of the conductor increases because the material’s intrinsic resistance to flow of electrons is higher. Copper wire has low resistivity but Nichrome wire has high resistivity.
Analogy – If the material flowing is oil instead of water it will take more time to flow due to higher viscosity.

OHM’S LAW

V = I R  ; where ‘V’ is the voltage across the conductor, ‘I’ is the current and ‘R’ the resistance of the conductor.

V the voltage is the push that moves the electrical charges from one end to the other, measured in volts (V)

I is the flow rate of electrical charge, measured in amperes (A)

R is the resistance or opposition to the flow of electrical charges, measured in ohms ( Ω)

In a circuit if two values are known you can find the unknown value –
To find Voltage use V= I.R
To find Current use I = V/R
To find Resistance use R = V/I

SERIES CIRCUIT

In a series circuit there is only one path for the current and current is the same in all the resistors. The net voltage gets divided among the individual resistors. The Equivalent resistance of series of resistors is given by
R_eq = R₁+R₂+R₃+…
Total or equivalent resistance is greater than the largest resistance.

After finding R_eq you can use the Ohm’s Law equation to find current in the circuit.

Analogy : Water flowing from tank A(at higher pressure/height) to tank B (lower pressure/height) through a single pipe having series of narrow different diameter sections (constrictions) in the path. There will be resistance to flow of water at every point and total resistance to flow is due to sum of all constrictions combined.

PARALLEL CIRCUIT

In a parallel circuit there are multiple paths for the current and current gets divided among the individual resistors. The net voltage is the same across the individual resistors. The Equivalent resistance of series of resistors is given by
1/R_eq = 1/R₁+1/R₂+1/R₃+…
Total or equivalent resistance is lesser than the smallest resistance.

After finding R_eq you can use the Ohm’s Law equation to find current in the circuit.

Analogy : Water is flowing from tank A (at higher pressure/height) to tank B (lower pressure/height) through 3 separate pipes of different diameters(constrictions). The total resistance to the flow of water will be less than the resistance of the narrowest pipe because, along with the water fighting through that tight squeeze, extra water is also flowing out through the other two pipes at the same time.”

Q&A on Ohm’s Law

Questions on finding unknown resistance (Hint use R = = V/I )

In a simple circuit consisting of 9 volts battery, resistor, ammeter and voltmeter –
Drag and drop the correct resistor to get 9 A current in the circuit. Answer:1 ohm
Drag and drop the correct resistor to get 4.5 A current in the circuit. Answer: 2 ohm
Drag and drop the correct resistor to get 3 A current in the circuit. Answer: 3 ohm
Drag and drop the correct resistor to get 1.8 A current in the circuit. Answer: 5ohm

In a simple circuit consisting of 6 volts battery, resistor, ammeter and voltmeter –
Drag and drop the correct resistor to get 6 A current in the circuit. Answer: 1 ohm
Drag and drop the correct resistor to get 3 A current in the circuit. Answer: 2 ohm
Drag and drop the correct resistor to get 2 A current in the circuit. Answer: 3 ohm
Drag and drop the correct resistor to get 1.2 A current in the circuit. Answer: 5 ohm

In a simple circuit consisting of 3 volts battery, resistor, ammeter and voltmeter –
Drag and drop the correct resistor to get 1.5 A current in the circuit. Answer: 2 ohm
Drag and drop the correct resistor to get 1 A current in the circuit. Answer: 3 ohm
Drag and drop the correct resistor to get 3 A current in the circuit, Answer: 1 ohm
Drag and drop the correct resistor to get 0.6 A current in the circuit. Answer: 5 ohm

In a simple circuit consisting of 1.5 volts battery, resistor, ammeter and voltmeter –
Drag and drop the correct resistor to get 1.5 A current in the circuit. Answer: 1 ohm
Drag and drop the correct resistor to get 0.75 A current in the circuit. Answer: 2 ohm
Drag and drop the correct resistor to get 0.5 A current in the circuit. Answer: 3 ohm
Drag and drop the correct resistor to get 0.3 A current in the circuit. Answer: 5 ohm

Questions on finding unknown voltage (Hint use V = I.R )

In a simple circuit consisting of a 1 ohm resistor, a battery, ammeter and voltmeter –
Drag in correct battery to get 1.5 A current in the circuit. Answer: 1.5 volts
Drag in correct battery to get 3 A current in the circuit.  Answer: 3 volts
Drag in correct battery to get 6 A current in the circuit. Answer: 6 volts
Drag in correct battery to get 9 A current in the circuit. Answer: 9 volts

In a simple circuit consisting of a 2 ohm resistor, a battery, ammeter and voltmeter –
Drag in correct battery to get 0.75 A current in the circuit. Answer: 1.5 volts
Drag in correct battery to get 1.5 A current in the circuit. Answer: 3 volts
Drag in correct battery to get 3 A current in the circuit. Answer: 6 volts
Drag in correct battery to get 4.5 A current in the circuit. Answer: 9 volts

In a simple circuit consisting of a 3 ohm resistor, a battery, ammeter and voltmeter –
Drag in correct battery to get 0.5 A current in the circuit. Answer: 1.5 volts
Drag in correct battery to get 1 A current in the circuit. Answer: 3 volts
Drag in correct battery to get 2 A current in the circuit. Answer: 6 volts
Drag in correct battery to get 3 A current in the circuit. Answer: 9 volts

In a simple circuit consisting of a 5 ohm resistor, a battery, ammeter and voltmeter –
Drag in correct battery to get 0.3 A current in the circuit. Answer: 1.5 volts
Drag in correct battery to get 0.6 A current in the circuit. Answer: 3 volts
Drag in correct battery to get 1.2 A current in the circuit. Answer: 6 volts
Drag in correct battery to get 1.8 A current in the circuit. Answer: 9 volts

Questions on finding unknown current (Hint use I = V/R )

The current in a circuit consisting of 1.5 volts battery and 1 ohm resistor will be?
Answer: 1.5 A
The current in a circuit consisting of 1.5 volts battery and 2 ohm resistor will be?
Answer: 0.75 A
The current in a circuit consisting of 1.5 volts battery and 3 ohm resistor will be?
Answer: 0.5 A
The current in a circuit consisting of 1.5 volts battery and 5 ohm resistor will be?
 Answer: 0.3 A
The current in a circuit consisting of 3 volts battery and 1 ohm resistor will be?
Answer: 3 A
The current in a circuit consisting of 3 volts battery and 2 ohm resistor will be?
Answer: 1.5 A
The current in a circuit consisting of 3 volts battery and 3 ohm resistor will be?
Answer: 1 A
The current in a circuit consisting of 3 volts battery and 5 ohm resistor will be?
Answer: 0.6 A
The current in a circuit consisting of 6 volts battery and 1 ohm resistor will be?
Answer: 6 A
The current in a circuit consisting of 6 volts battery and 2 ohm resistor will be?
Answer: 3 A
The current in a circuit consisting of 6 volts battery and 3 ohm resistor will be?
Answer: 2 A
The current in a circuit consisting of 6 volts battery and 5 ohm resistor will be?
Answer: 1.2 A
The current in a circuit consisting of 9 volts battery and 1 ohm resistor will be?
Answer: 9 A
The current in a circuit consisting of 9 volts battery and 2 ohm resistor will be?
Answer: 4.5 A
The current in a circuit consisting of 9 volts battery and 3 ohm resistor will be?
Answer: 3 A
The current in a circuit consisting of 9 volts battery and 5 ohm resistor will be?
Answer: 1.8 A

Q&A on SERIES CIRCUITS

You are given a pair of 1 ohm, 2 ohm, 3 ohm and 5 ohm resistors.

Questions on finding unknown resistance (Hint find R_eq using R = V/I ; and then select R₁ and R₂ to fit in R_eq = R₁ +R₂ )

Complete the series circuit consisting of 1.5 volts battery by adding two resistors so as to get current of 0.5 A in the circuit?
Answer: 1 ohm and 2 ohm
Complete the series circuit consisting of 1.5 volts battery by adding two resistors so as to get current of 0.75 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the series circuit consisting of 3 volts battery by adding two resistors so as to get current of 0.3 A in the circuit?
Answer: 5 ohm and 5 ohm
Complete the series circuit consisting of 3 volts battery by adding two resistors so as to get current of 0.5 A in the circuit?
Answer: 3 ohm and 3 ohm or 1 ohm and 5 ohm
Complete the series circuit consisting of 3 volts battery by adding two resistors so as to get current of 1 A in the circuit?
Answer: 1 ohm and 2 ohm
Complete the series circuit consisting of 3 volts battery by adding two resistors so as to get current of 1.5 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the series circuit consisting of 6 volts battery by adding two resistors so as to get current of 0.6 A in the circuit?
Answer: 5 ohm and 5 ohm
Complete the series circuit consisting of 6 volts battery by adding two resistors so as to get current of 1 A in the circuit?
Answer: 3 ohm and 3 ohm or 1 ohm and 5 ohm
Complete the series circuit consisting of 6 volts battery by adding two resistors so as to get current of 1.5 A in the circuit?
Answer: 2 ohm and 2 ohm or 1 ohm and 3 ohm
Complete the series circuit consisting of 6 volts battery by adding two resistors so as to get current of 2 A in the circuit?
Answer: 1 ohm and 2 ohm
Complete the series circuit consisting of 6 volts battery by adding two resistors so as to get current of 3 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the series circuit consisting of 9 volts battery by adding two resistors so as to get current of 0.9 A in the circuit?
Answer: 5 ohm and 5 ohm
Complete the series circuit consisting of 9 volts battery by adding two resistors so as to get current of 3 A in the circuit?
Answer: 1 ohm and 2 ohm
Complete the series circuit consisting of 9 volts battery by adding two resistors so as to get current of 4.5 A in the circuit?
Answer: 1 ohm and 1 ohm

Questions on finding unknown current (Hint first find R_eq = R₁ +R₂ and then use I = V/R )

The current in a series circuit consisting of 1.5 volts battery and two 5 ohm resistors will be?
Answer: 0.15 A
The current in a series circuit consisting of 1.5 volts battery and two 3 ohm resistors will be?
Answer: 0.25 A
The current in a series circuit consisting of 1.5 volts battery and a 1 ohm and a 5 ohm resistor will be?
Answer: 0.25 A
The current in a series circuit consisting of 1.5 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 0.3 A
The current in a series circuit consisting of 3 volts battery and two 2 ohm resistors will be?
Answer: 0.75 A
The current in a series circuit consisting of 3 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 0.6 A
The current in a series circuit consisting of 3 volts battery and a 1 ohm and a 3 ohm resistor will be?
Answer: 0.75 A
The current in a series circuit consisting of 6 volts battery and a 1 ohm and a 3 ohm resistor will be?
Answer: 1.5 A
The current in a series circuit consisting of 6 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 1.2 A
The current in a series circuit consisting of 6 volts battery and a 5 ohm and a 3 ohm resistor will be?
Answer: 0.75 A
The current in a series circuit consisting of 9 volts battery and two 3 ohm resistors will be?
Answer: 1.5 A
The current in a series circuit consisting of 9 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 1.8 A
The current in a series circuit consisting of 9 volts battery and a 1 ohm and a 5 ohm resistor will be?
Answer: 1.5 A

Q&A on PARALLEL CIRCUITS

You are given a pair of 1 ohm, 2 ohm, 3 ohm and 5 ohm resistors.

Questions on finding unknown resistance (Hint find R_eq using R = V/I ; and then select R₁ and R₂ to fit R_eq = R₁ x R₂/(R₁ + R₂ )

Complete the parallel circuit consisting of 1.5 volts battery by adding two resistors so as to get current of 1 A in the circuit?
Answer: 3 ohm and 3 ohm
Complete the parallel circuit consisting of 1.5 volts battery by adding two resistors so as to get current of 1.5 A in the circuit?
Answer: 2 ohm and 2 ohm
Complete the parallel circuit consisting of 1.5 volts battery by adding two resistors so as to get current of 3 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the parallel circuit consisting of 3 volts battery by adding two resistors so as to get current of 6 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the parallel circuit consisting of 3 volts battery by adding two resistors so as to get current of 3 A in the circuit?
Answer: 2 ohm and 2 ohm
Complete the parallel circuit consisting of 3 volts battery by adding two resistors so as to get current of 2 A in the circuit?
Answer: 3 ohm and 3 ohm
Complete the parallel circuit consisting of 6 volts battery by adding two resistors so as to get current of 12 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the parallel circuit consisting of 6 volts battery by adding two resistors so as to get current of 6 A in the circuit?
Answer: 2 ohm and 2 ohm
Complete the parallel circuit consisting of 6 volts battery by adding two resistors so as to get current of 4 A in the circuit?
Answer: 3 ohm and 3 ohm
Complete the parallel circuit consisting of 9 volts battery by adding two resistors so as to get current of 18 A in the circuit?
Answer: 1 ohm and 1 ohm
Complete the parallel circuit consisting of 9 volts battery by adding two resistors so as to get current of 9 A in the circuit?
Answer: 2 ohm and 2 ohm
Complete the parallel circuit consisting of 9 volts battery by adding two resistors so as to get current of 6 A in the circuit?
Answer: 3 ohm and 3 ohm

Questions on finding unknown current (Hint first find R_eq = R₁ x R₂/(R₁ + R₂ ) and then use I = V/R )
The current in a parallel circuit consisting of 1.5 volts battery and two 5 ohm resistors will be?
Answer: 0.6 A
The current in a parallel circuit consisting of 1.5 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 1.25 A
The current in a parallel circuit consisting of 1.5 volts battery and a 1 ohm and a 3 ohm resistor will be?
Answer: 2 A
The current in a parallel circuit consisting of 3 volts battery and two 5 ohm resistors will be?
Answer: 1.2 A
The current in a parallel circuit consisting of 3 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 2.5 A
The current in a parallel circuit consisting of 3 volts battery and a 1 ohm and a 3 ohm resistor will be?
Answer: 4 A
The current in a parallel circuit consisting of 6 volts battery and two 5 ohm resistors will be?
Answer: 2.4 A
The current in a parallel circuit consisting of 6 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 5 A
The current in a parallel circuit consisting of 6 volts battery and a 1 ohm and a 3 ohm resistor will be?
Answer: 8 A
The current in a parallel circuit consisting of 9 volts battery and two 5 ohm resistors will be?
Answer: 3.6 A
The current in a parallel circuit consisting of 9 volts battery and a 2 ohm and a 3 ohm resistor will be?
Answer: 7.5 A
The current in a parallel circuit consisting of 9 volts battery and a 1 ohm and a 3 ohm resistor will be?
Answer: 12 A