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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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

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A rectangular loop of size 5 cm $\times$ 8 cm is lying in the $x$-$y$ plane in a uniform magnetic field $\vec{B} = (2.0\ \text{T})\hat{k}$. The total magnetic flux linked with the loop is:

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A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

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In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

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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.A rectangular loop of size 5 cm $\times$ 8 cm is lying in the $x$-$y$ plane in a uniform magnetic field $\vec{B} = (2.0\ \text{T})\hat{k}$. The total magnetic flux linked with the loop is:

2.A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

4.In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

5.Find the ratio $\dfrac{\lambda_\alpha}{\lambda_p}$ of the de Broglie wavelength $\lambda_\alpha$ associated with an alpha particle to the de Broglie wavelength $\lambda_p$ associated with a proton if both are moving with the same velocity.

6.A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

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Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A rectangular loop of size 5 cm $\times$ 8 cm is lying in the $x$-$y$ plane in a uniform magnetic field $\vec{B} = (2.0\ \text{T})\hat{k}$. The total magnetic flux linked with the loop is:

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A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

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In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

5.
Find the ratio $\dfrac{\lambda_\alpha}{\lambda_p}$ of the de Broglie wavelength $\lambda_\alpha$ associated with an alpha particle to the de Broglie wavelength $\lambda_p$ associated with a proton if both are moving with the same velocity.

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