The current -i- in a circuit containing resistance R -10 - and inductive reactance X L -7-5 - varies with time -t- as shown in the figure- The average power consumed in the circuit isA- 291 WB- 175 WC- 250 WD- 96 W

The correct option is D 96 WThe equation of current is given as i=2+4 sin(ω t+ϕ ) i_rms=√(∫^T_0[2+4sin (ω t+ϕ )]^2dt/T) i_rms=2√(3)A Heat produced per second ...

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Standard XII

Physics

Turns Ratio

The current '...

Question

The current 'i' in a circuit containing resistance $R = 10 Ω$ and inductive reactance $X_{L} = 7.5 Ω$ varies with time 't' as shown in the figure. The average power consumed in the circuit is

96 W

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291 W

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175 W

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250 W

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Solution

The correct option is A 96 W
The equation of current is given as
$i = 2 + 4 s i n (ω t + ϕ)$
$i_{r m s} = \sqrt{\frac{\int_{0}^{T} [2 + 4 s i n (ω t + ϕ)]^{2} d t}{T}} i_{r m s} = 2 \sqrt{3} A$
Heat produced per second = $(2 \sqrt{3})^{2} \times 10 \times \frac{4}{5} = 96 W$

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The current 'i' in a circuit containing resistance R=10 Ω and inductive reactance XL=7.5 Ω varies with time 't' as shown in the figure. The average power consumed in the circuit is

The correct option is A 96 WThe equation of current is given as i=2+4 sin(ωt+ϕ) irms=√∫T0[2+4sin (ω t+ϕ)]2dtTirms=2√3A Heat produced per second = (2√3)2×10×45=96 W

The current 'i' in a circuit containing resistance $R = 10 Ω$ and inductive reactance $X_{L} = 7.5 Ω$ varies with time 't' as shown in the figure. The average power consumed in the circuit is

The correct option is A 96 W
The equation of current is given as
$i = 2 + 4 s i n (ω t + ϕ)$
$i_{r m s} = \sqrt{\frac{\int_{0}^{T} [2 + 4 s i n (ω t + ϕ)]^{2} d t}{T}} i_{r m s} = 2 \sqrt{3} A$
Heat produced per second = $(2 \sqrt{3})^{2} \times 10 \times \frac{4}{5} = 96 W$