Two bulbs rated (P1, V) and (P2, V) are connected (i) in series and (ii) in parallel across supply V. Determine power in the two combinations P1 and P2.

Electric power can be defined as the rate at which work is done or energy is converted into an electric circuit. In other words, it is the measurement energy used in a span of time.

Step 1:Formula

Electric Power formula is given by:

P = VI

Here (in the circuit),

P = Power
V = Potential Difference
I = Electric Current

Power is often also denoted as,

⇒ P = I²R
⇒ $P = {{V^2} \over R}$
$\therefore$ Expressions above are determined using Ohm’s Law, wherein, Voltage, current, and resistance are interrelated by the relation:

V = IR

Here (in the circuit),

R = Resistance
V = Potential Difference
I = Electric Current

Step 2: Solution

(i) Two bulbs of (P1, V) and (P2, V) that are connected in series:

The flow of current in both bulbs is the same. Assuming R1 and R2 are both resistances of the bulbs, then the effective resistance circuit:

⇒ R = R1 + R2

Now, after using the relation, we can obtain:

P=V²/R

And, R = V²/P

Therefore, V²/P = V1²/ P1 + V2²/P2

As is given, V₁ = V₂ = V.

Therefore,

⇒ 1/P = 1/P₁ + 1/P₂

Hence, effective power of two bulbs connected in series is 1/ P = 1 / P₁ + 1 / P₂

(ii) Two bulbs of (P1, V) and (P2, V) when connected in parallel:

⇒ 1/R = 1/R₁ + 1/R₂

We know that

P = V²/R

1/R = V²/P

As is given, V1 = V2

Thus, P/V2 = P1/V² + P2/V²

Hence, the effective power of two bulbs connected in parallel is P = P₁ + P₂.

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View Solution

Two bulbs rated (P1, V) and (P2, V) are connected (i) in series and (ii) in parallel across supply V. Determine power in the two combinations P1 and P2.

Step 1:Formula

Step 2: Solution

CBSE CLASS XII Related Questions

1.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

2.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

3.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

5.
This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

6.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

Similar Physics Concepts

Comments

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Two bulbs rated (P1, V) and (P2, V) are connected (i) in series and (ii) in parallel across supply V. Determine power in the two combinations P1 and P2.

Step 1:Formula

Step 2: Solution

CBSE CLASS XII Related Questions

1. The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

2.A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

3.Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

5.This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

6.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

2.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

3.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

5.
This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

6.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?