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प्रश्न
Obtain the expression for the applied emf and the effective resistance of the circuit when alternating emf is applied to a CR circuit.
उत्तर
- Consider an alternating e.m.f. applied to a series combination of the pure capacitor of capacitance C and resistor of resistance R.
- Let eR and eC be the r.m.s. the voltage across the resistor and capacitor respectively. As R and C are in series, the current at any instant is given as i = i0 sin ωt.
- Vector diagram,
- From the above figure,
e2 = `"e"_"R"^2 + "e"_"C"^2`
∴ e = `sqrt("e"_"R"^2 + "e"_"C"^2) = sqrt(("iR")^2 + ("iX"_"C")^2) = "i"sqrt("R"^2 + "X"_"C"^2)`
∴ e = iZ
where Z = `sqrt("R"^2 + "X"_"C"^2)` is the impedance of the RC circuit. - a. Expression for applied emf in CR circuit,
e = e0sinωt = `sqrt("e"_"R"^2 + "e"_"C"^2)` = iZ
b. Expression for effective resistance in CR circuit, Z = `sqrt("R"^2 + "X"_"C"^2)`
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