Chapter 18 Alternating Current Circuits

A pure resistor is connected to an a.c. source where its current is given by I=5.0 sin 628t. Which of the following statements is not true about the circuit?

• The peak value of current flowing through the resistor is 5.0 A

• The root mean square current flowing through the resistor is 3.5 A

• The frequency of the current flowing through across the resistor is 120 Hz

• The equivalent direct current which gives the same average heating power in the resistor is 3.5 A

Which of the following statements is not true about the above circuit?

• The instantaneous current in the circuit is I=I0 sin $\omega t$

• The peak value of the alternating current is $\frac{V_0}{R}$

• The impedance of the circuit is $\omega R$

• The hot-wire ammeter in the circuit can also be used to measure the direct current

• A

• B

• C

• D

Find the ratio of  $\frac{mean\ power\ dissipated\ through\ R\ in\ \left(a\right)}{power\ dissipated\ through\ R\ in\ \left(b\right)}$  

• 2

•  $\frac{1}{2}$  

• 4

•  $\frac{1}{4}$  

An inductor of inductance 22.0 mH is connected to an a.c. supply with frequency f. If the reactance of the inductor is 660 Ω, what is the value of f?

• 1.45 $\times10^3\$ Hz

• 3.00 $\times10^3\$ Hz

• 4.77 $\times10^3\$ Hz

• 7.16 $\times10^3\$ Hz

The variation of voltage across an inductor with time t in an a.c. circuit is as shown in the graph. Which graphs shows the variation of the current I which flows through the inductor with time t?

• 
• 
• 
• 

A pure inductor is connected to an a.c. source of frequency 100 Hz and the r.m.s. value of the voltage is 12 V. If the peak value of the current flowing through the inductor is 14 A, what is the inductance of the inductor?

• 1.6 mH

• 1.9 mH

• 30 mH

• 39 mH

A pure inductor of inductance 15 H is connected to an a.c.s source of frequency 100 Hz. If the r.m.s. value of the voltage is 12 V, what is the maximum instantaneous output power?

• 1.3 $\times10^{-3}W$

• 1.5 $\times10^{-2}W$

• 0 W

• 1.5 W

A pure capacitor of capacitance C is connected to an a.c. supply of peak voltage V₀. Which pair of expressions below are for the voltage and current in the circuit?

• $V=V_0\ \sin\ \left(\omega t+\frac{\pi}{2}\right)$ $I=I_0\ \sin\omega t$

• $V=V_0\ \sin\ \left(\omega t+\frac{\pi}{2}\right)$ $I=I_0\ \cos\ \omega t$

• $V=V_0\ \sin\ \omega t$ $I=I_0\cos\ \omega t$

• $V=V_0\ \sin\ \omega t$ $I=I_0\ \sin\ \omega t$

A pure capacitor is connected to an a.c. supply of frequency 50 Hz and r.m.s. voltage 6.0 V. If the r.m.s. value of the current in the circuit is 30 mA, what is the capacitance of the capacitor?

• 13 $\mu$ F

• 14 $\mu$ F

• 15 $\mu$ F

• 16 $\mu$ F