An AC source producing emf $$\epsilon = \epsilon_0[ cos(100 \pi S^{-1})t + cos (500 \pi s^{-1})t]$$ is connected in series with a capacitor and a resister. The steady-state current in the circuit is found to be:
$$i = i_1 [cos(100 \pi s^{-1})t + \phi_1] + i_1 cos[(500 \pi s^{-1})t + \phi_1]$$

$$i_1 < i_2$$

$$i_1 > i_2$$

the information is insufficient to find the relation between $$i_1$$ and $$i_2$$.

$$i_1 = i_2$$

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Solution

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Correct option is C. $$i_1 < i_2$$

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An AC source producing emf $$\epsilon = \epsilon_0[ cos(100 \pi S^{-1})t + cos (500 \pi s^{-1})t]$$ is connected in series with a capacitor and a resister. The steady-state current in the circuit is found to be:
$$i = i_1 [cos(100 \pi s^{-1})t + \phi_1] + i_1 cos[(500 \pi s^{-1})t + \phi_1]$$

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A C

source producing emf

E = E_{0} [c o s (100 π s^{- 1}) t] + E_{0} c o s [(500 π s^{- 1}) t]

is connected in series with a capacitor and a resistance, the steady state current in the circuit is found to be

i = i_{1} [c o s (100 π s^{- 1}) t + φ_{1}] + i_{2} c o s [(500 π s^{- 1}) t + φ_{2}]

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An AC source producing emf
ε = ε₀ [cos (100 π s⁻¹)t + cos (500 π s⁻¹)t]
is connected in series with a capacitor and a resistor. The steady-state current in the circuit is found to be i = i₁ cos [(100 π s⁻¹)t + φ₁) + i₂ cos [(500π s⁻¹)t + ϕ₂]. So,

(a) i₁ > i₂
(b) i₁ = i₂
(c) i₁ < i₂
(d) The information is insufficient to find the relation between i₁ and i₂.

View Solution

A C

source producing emf$in ={ in }_{ 0 } [ \cos { \left( 10\pi { s }^{ -1 } \right) t+ \left[ \cos { \left( 500\pi { s }^{ -1 } \right) t } \right]

i s c o n n e c t e d i n s e r i e s w i t h a c a p a c i t o r a n d a r e s i s t o r . T h e s t e a d y s t a t e c u r r e n t i n t h e c i r c u i t i s f o u n d t o b e

i={ i }_{ 1 }\cos { \left[ \left( 100\pi { s }^{ -1 } \right) t+{ \varphi }_{ 1 } \right] +{ i }_{ 2 }\cos { \left[ \left( 500\pi { s }^{ -1 } \right) t+{ \phi }_{ 2 } \right] } }$

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An AC source producing emf

ϵ = ϵ_{0} [cos (100 Π s^{- 1}) + cos (500 Π s^{- 2}) t]

is connected in series with a capacitor and a resistor. The steady state current in the circuit is found to be

i = i_{1} [cos (100 Π s^{- 1}) t + ϕ] + i_{2} cos [500 Π s^{- 1}) t + ϕ]

relation between

i_{1}

and

i_{2} = ?

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An AC source producing emf $$\epsilon = \epsilon_0[ cos(100 \pi S^{-1})t + cos (500 \pi s^{-1})t]$$ is connected in series with a capacitor and a resister. The steady-state current in the circuit is found to be:$$i = i_1 [cos(100 \pi s^{-1})t + \phi_1] + i_1 cos[(500 \pi s^{-1})t + \phi_1]$$

Correct option is C. $$i_1 < i_2$$

An AC source producing emf $$\epsilon = \epsilon_0[ cos(100 \pi S^{-1})t + cos (500 \pi s^{-1})t]$$ is connected in series with a capacitor and a resister. The steady-state current in the circuit is found to be:
$$i = i_1 [cos(100 \pi s^{-1})t + \phi_1] + i_1 cos[(500 \pi s^{-1})t + \phi_1]$$