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But to hear one particular radio station, we tune the radio. In tuning, wevary the capacitance of a capacitor in the tuning circuit such that theresonant frequency of the circuit becomes nearly equal to the frequencyof the radio signal received. When this happens, the amplitude of thecurrent with the frequency of the signal of the particular radio station inthe circuit is maximum.It is important to note that resonance phenomenon is exhibited by acircuit only if both L and C are present in the circuit. Only then do thevoltages across L and C cancel each other (both being out of phase)and the current amplitude is v m/R, the total source voltage appearingacross R. This means that we cannot have resonance in a RL or RCcircuit.Sharpness of resonanceThe amplitude of the current in the series LCR circuit is given byim=Rvm⎛ ⎞+ ⎜ωL −⎝ ω C ⎟⎠2 12and is maximum when ω = ω0 = 1/ LC.The maximum value isi = v R.maxm m /For values of ω other than ω 0, the amplitude of the current is lessthan the maximum value. Suppose we choose a value of ω for which thecurrent amplitude is 1/ 2 times its maximum value. At this value, thepower dissipated by the circuit becomes half. From the curve inFig. (7.16), we see that there are two such values of ω, say, ω 1and ω 2, onegreater and the other smaller than ω 0and symmetrical about ω 0. We maywriteω 1= ω 0+ Δωω 2= ω 0– ΔωThe difference ω 1– ω 2= 2Δω is often called the bandwidth of the circuit.The quantity (ω 0/ 2Δω) is regarded as a measure of the sharpness ofresonance. The smaller the Δω, the sharper or narrower is the resonance.To get an expression for Δω, we note that the current amplitude i mismax( 1/ 2) i mwww.GOALias.blogspot.comfor ω 1= ω 0+ Δω. Therefore,Alternating Currentat ω ,1im=R2vm⎛ 1 ⎞+ ⎜ω1L−ω1C⎟⎝⎠2maximvm= =2 R 2249