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.

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 ?

3.Write two advantages of reflecting telescope over refracting telescope.

4.Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

6.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.

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 ?

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4.
Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

6.
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.