Answer
Verified
38.4k+ views
Hint: In this question, the given circuit is RLC and AC source is applied, so the concept of the resultant voltage concept will be used that is induction voltage and the capacitance voltage are at same phase while the resistance voltage are at perpendicular phase.
Complete step by step answer:
A standard RLC circuit consists of a resistor, an inductor and a capacitor in series. We consider the voltage across the resistor \[{V_R}\], the voltage across the inductor \[{V_L}\], and the voltage across the capacitor to be \[{V_c}\].
Now this type of circuit has a specific frequency at which it resonates. That is called the resonating frequency.
So, the standard formula to be used in simple series RLC circuit is-
\[ \Rightarrow {V_e} = \sqrt {V_R^2 + {{\left( {{V_L} - {V_C}} \right)}^2}} \]
From the given circuit, we have ${V_R}$ is $30\;{\text{V}}$, ${V_L}$ is $60\;{\text{V}}$, and ${V_C}$ is $100\;{\text{V}}$. Now, we substitute the given values in the above equation as,
\[ \Rightarrow {V_e} = \sqrt {{{30}^2} + {{\left( {60 - 100} \right)}^2}} \]
Now, we simplify the above equation as,
\[ \Rightarrow {V_e} = \sqrt {{{30}^2} + {{\left( { - 40} \right)}^2}} \]
After calculation we get the result as,
\[\therefore V = 50V\]
Hence, the voltage from the emf source obtained across the series combination of the given RLC circuit is \[50V\].
Thus, the correct option is C.
Note: We have seen that the three basic components in a circuit are Resistance, Inductance, and Capacitance have very different phase relationships to each other when connected to a sinusoidal alternating supply which in this case is the source of the emf given. The negative sign in the formula of the net voltage indicates that the inductor is ahead of the capacitance by some degrees phase angle. If the circuit is completely a resistor circuit then the difference in voltages of the other two would have been zero. The resistance of an inductor is \[L\omega \], and that of capacitor is \[\dfrac{1}{{C\omega }}\], where \[C\] is the capacitance and \[L\] is the inductance provided.
Complete step by step answer:
A standard RLC circuit consists of a resistor, an inductor and a capacitor in series. We consider the voltage across the resistor \[{V_R}\], the voltage across the inductor \[{V_L}\], and the voltage across the capacitor to be \[{V_c}\].
Now this type of circuit has a specific frequency at which it resonates. That is called the resonating frequency.
So, the standard formula to be used in simple series RLC circuit is-
\[ \Rightarrow {V_e} = \sqrt {V_R^2 + {{\left( {{V_L} - {V_C}} \right)}^2}} \]
From the given circuit, we have ${V_R}$ is $30\;{\text{V}}$, ${V_L}$ is $60\;{\text{V}}$, and ${V_C}$ is $100\;{\text{V}}$. Now, we substitute the given values in the above equation as,
\[ \Rightarrow {V_e} = \sqrt {{{30}^2} + {{\left( {60 - 100} \right)}^2}} \]
Now, we simplify the above equation as,
\[ \Rightarrow {V_e} = \sqrt {{{30}^2} + {{\left( { - 40} \right)}^2}} \]
After calculation we get the result as,
\[\therefore V = 50V\]
Hence, the voltage from the emf source obtained across the series combination of the given RLC circuit is \[50V\].
Thus, the correct option is C.
Note: We have seen that the three basic components in a circuit are Resistance, Inductance, and Capacitance have very different phase relationships to each other when connected to a sinusoidal alternating supply which in this case is the source of the emf given. The negative sign in the formula of the net voltage indicates that the inductor is ahead of the capacitance by some degrees phase angle. If the circuit is completely a resistor circuit then the difference in voltages of the other two would have been zero. The resistance of an inductor is \[L\omega \], and that of capacitor is \[\dfrac{1}{{C\omega }}\], where \[C\] is the capacitance and \[L\] is the inductance provided.
Recently Updated Pages
silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main
A parallel plate capacitor has a capacitance C When class 12 physics JEE_Main
Let gx 1 + x x and fx left beginarray20c 1x 0 0x 0 class 12 maths JEE_Main
A series combination of n1 capacitors each of value class 12 physics JEE_Main
When propyne is treated with aqueous H2SO4 in presence class 12 chemistry JEE_Main
Which of the following is not true in the case of motion class 12 physics JEE_Main
Other Pages
The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
Dissolving 120g of urea molwt60 in 1000g of water gave class 11 chemistry JEE_Main
A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main
when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main