Relation between Power and Resistance Important Questions

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Short Answer Questions [2 Marks Question]

Ques. Find the equivalent resistance for a circuit where R1 = 15Ω, R2 20Ω, and R3 = 30Ω are in a series arrangement.

Ans. For a series arrangement of resistors, the equivalent resistance is: 

R_S = R₁ + R₂ + R₃ 

R_S = 15Ω + 20Ω + 30Ω

R_S = 65Ω

Ques. What is the resistance of an object? 

Ans. The resistance of an object is the measure of how much it opposes the flow of current. It is calculated in ohms. The amount of opposition to the flow of current can be increased by combining two or more resistances in a series or parallel arrangement. 

Ques. What are the factors affecting resistance?

Ans. The following factors can affect the Resistance of a conductor-

• Length of the conductor
• Cross-sectional area of the conductor.
• Temperature of the conducting material
• Conductor's material 

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Long Answer Questions [3 Marks Question]

Ques. With the same emf of 10 V, a combination of two batteries with different internal resistances of 20 ohm and 5 ohm, is attached to a parallel combination of 30 ohm and R ohm. Find the value of R.

As per the question, The emf of two batteries = 10 V

• Internal resistances of Two batteries = 20 Ω and 5 Ω
• Parallel combination = 30 Ω and R Ω.
• Voltage Difference across the battery of internal resistance 20 Ω = 0

Parallel Combination of Resistors

Value of R:

E1 = E – ir 

E2 = E – ir

= 10 – i20 = 0

= 10 – 0.5 × 5

i = 0.5 A

= 7.5 V

Thus,

E1 + E2 = 7.5 V

i =( i1 + i2)

⇒ 0.5 = (7.5/x) + (7.5/30)

⇒ R = 30 Ω

Ques. What is ohm's law?

Ans,  Ohm’s law states that voltage across a conductor is proportional to the current flowing through it, considering all physical conditions and temperatures remain constant. Ohm’s Law links voltage (V) and current (I) to the properties of the conductor, that is its resistance (r) in a circuit. The most basic and important law of electric circuits is the Ohm's Law.

Mathematically, Ohm's Law is written as:

V = I * R

Where, 

• V is the Voltage (Potential Difference) measured in Volts. 

To find voltage (V),

[V = I x R] V(volts) = (amps) x R(Ω)

• It is the current flowing through the conductor.

To Find the current (I),

[I = V / R] I(amps) = V(volts) + R(Ω)

• R is the resistance of the circuit measured in Ohms (Ω).

To find the resistance (R), 

[R = V / I] R= V volts) / I(amps)

Ques. A 220 V, 100W bulb is connected to a 110 V source. Calculate the power consumed by the bulb?

Ans. V= Potential difference(V), R= Resistance and I= current.

In the question, Potential difference= 220 V, Power of the bulb= 100W, Voltage= 110V

Resistance of the bulb

⇒ R = \(\frac{v^2}{P}\) = \(\frac{(220)^2}{100}\) = 484Ω

Power consumed

⇒ P = \(\frac{v^2}{R}\) = \(\frac{(110)^3}{100}\) =25 W

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Very Long Answer Questions [5 Marks Question]

Ques. Two identical resistors with resistances 15 ohm are connected in series and parallel to a battery of 6 V. Calculate ratio of power consumed.

Ans. In order to calculate the ratio of the power consumed in the combination of resistors in each case, we have to:

Resistance of two identical resistors, R1 = R2 = 15Ω

Voltage of battery, V = 6V.

Now, in order to determine the ratio of power that is consumed in the combination of resistors in each case, PS/PR.

1. In Series combination

In series, total resistance can be represented as:

RS = R1 + R2

After replacing the values,

⇒ RS = 15 + 15

⇒ RS = 30Ω

Therefore, total resistance in series, RS is 30Ω 

Now, we are already aware that the power consumed by a resistor can be denoted as:

P= \(\frac{V}{R}\)

Thus, Replacing the values of V and R, we can obtain:PS = 62/30

⇒ PS = 36/30

⇒ PS = 1.2W

Hence, the power that is consumed in series, PS is 1.2 watt.

2. In Parallel combination: 

In a parallel combination, the total resistance can be given as:

1/RP = 1/R1 + 1/R2 

After replacing the values,

⇒ 1/RP = 1/15 + 1/15

⇒ 1/RP = 1 + 1/15

⇒ 1/RP = 2/15

⇒ RP = 15/2

⇒ RP = 7.5Ω

Therefore, effective resistance in parallel combination, RP is 7.5Ω.

Replacing the values of V and R, we can obtain:

PR = 62/7.5

PR = 36/7.5

PR = 360/75

PR = 4.8W

Hence, power consumed in a parallel combination, PR is 4.8 watt (W). 

With the given data, the ratio of power consumed in the two combinations will be,

PS/PR = 1.2 W/4.8

W = 1/4 = 1:4 

Hence, the ratio of power consumed in the combination of resistors in both cases is 1:4.

Ques. Two resistors X and Y with 2 ohm and 3 ohm resistances respectively are first connected parallelly and then in series. In both cases, the voltage supplied is 5V.

(i) Draw the circuit diagram in order to depict the combination of resistors:

(ii) Estimate voltage across the 3 Ω resistor in the series combination of resistors.

1. Resistance of X = R1 = 2Ω
2. Resistance of Y = R2 = 3Ω
3. Voltage, V = 6V

Ans. In order to find the voltage across a 3Ω resistor in the series combination of resistors, we have to

We are already aware that the equivalent resistance (total resistance) in a series combination can be expressed as:

Req = R1 + R2

Now, after replacing the values of R1 and R2 we will get:

⇒ Req= 2 + 3

⇒ Req = 5Ω

We know that current can be expressed as:

I = V/R

Here, I = V/Req

So, inserting the given values, we will get:

I = 55

I = 1A

The current passing through the circuit is 1A.

Now, in order to find the voltage present across 3Ω resistors, we can also use the formula of voltage:

V = I × R

Now, after placing the required values, we get:

⇒ V = 1 × 3

⇒ V = 3V

Hence, the voltage across the 3Ω resistor is 3 Volts.

Ques. What does resistivity of a material depend on? 

Ans. The Resistivity of material depends on:

• The resistivity of a material depends on its nature and the temperature of the conductor.
• The resistivity of a material doesn't depend on its shape and size (length and area).
• Materials that conduct electrical current easily are called conductors and have a low resistivity.
• Materials that do not conduct electricity easily are called insulators and these materials have a high resistivity.
• Resistivity is the number of free electrons per unit volume of the conductor and the average relaxation time a conductor has in free electrons.
• Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.The unit for resistivity is ohm-meter (Ω-m).

Ques. Determine the following from an electric circuit

a) Effective resistance of 8 ohm resistors combination

b) Flowing current via 4 ohm resistor

Ans. Schematic representation of the circuit is: 

Schematic Representation 

1. There are two 8Ω resistors that are parallelly connected with one another, therefore their effective resistance equals:

⇒ 1/RP = 1/8 + 1/R

⇒ 1/RP = 1/4

8-ohm Resistors Combination

⇒ RP = 4Ω

Total Resistance

⇒ R = 4Ω + RP

⇒ R = 4Ω + 4Ω

⇒ R = 8Ω

Current Passing Via the Circuit

The current that passes through the circuit

⇒ I = V/R

⇒ I = 8/8

⇒ I = 1 A

Hence, the current that passes through a 4Ω resistor is 1A. Since 4Ω and Rp are connected in series as the same current flows through them.

2. Potential Difference across 4Ω resistor is

⇒ V = I × R

⇒ V = 1 × 4

⇒ V = 4V

Power in a 4Ω Resistor:

⇒ P = I2R

⇒ P = 12 × 4

⇒ P = 4 W

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