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

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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, P_S/P_R.

In case of Series combination

In series, total resistance can be represented as:

R_S = R1 + R2

After replacing the values,

⇒ R_S = 15 + 15

⇒ R_S = 30Ω

Therefore, total resistance in series, R_S is 30Ω

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

Power = Voltage²/Resistance

Or,

P = V²/R

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

P_S = 6²/30

⇒ P_S = 36/30

⇒ P_S = 1.2W

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

In case of Parallel combination:

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

1/R_P = 1/R₁ + 1/R₂

After replacing the values,

⇒ 1/R_P = 1/15 + 1/15

⇒ 1/R_P = 1 + 1/15

⇒ 1/R_P = 2/15

⇒ R_P = 15/2

⇒ R_P = 7.5Ω

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

Now, we are already aware that the power consumed by a resistor is expressed as:

Power = Voltage²/Resistance Or, P=V²/R

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

P_R = 6²/7.5

P_R = 36/7.5

P_R = 360/75

P_R = 4.8W

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

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

P_S/P_R= 1.2 W/4.8

Hence, W = 1/4 = 1:4

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

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

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

Related Questions

CBSE CLASS XII Related Questions

2.If T is the time period of the rotation of the coil, at what values of t in a cycle, the emf generator is maximum ?

4.Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power.

6.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.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
If T is the time period of the rotation of the coil, at what values of t in a cycle, the emf generator is maximum ?

4.
Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power.

6.
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.