Thus, a capacitor will resist changes in the potential difference across it because it requires a time for the potential difference to change by vC. The potential difference t across the capacitor decreases when it discharges and increases when charging. The larger the value of the slower the change in potential. If is then to a good C, t “small”, approximation, the potential difference across the capacitor at time is t An inductor can be considered to be a coil of wire. When a varying current passes through a coil, a varying magnetic flux is produced and this in turn induces a potential difference across the inductor. This induced potential difference opposes the change in current. The potential difference across the inductor is proportional to the rate of change of the current, where the constant of proportionality is known as the L inductance of the coil (henries H) and is given by the equation = di/dt vL L This equation can be expressed in terms of differences, = / L iL(t) vL(t) t Thus, an inductor will resist changes in the current through it because it requires a time for the current to change by If t is then to a good approximation, the t i. “small”, current through the inductor at time is t SERIES RC CIRCUIT Kirchhoff’s Laws with the equation can be used to compute the response of a series RC circuit for different applied emfs. The first step is calculate the applied emf and then specify the initial values for the vs variables for voltage current powers and energies v, i, p u. vS(0) = 0 assume capacitor is initially discharged vC(0) = { } / i(0) vS(0) vC(0) R – = vR(0) i(0) R = = i(0) = pS(0) vS(0) i(0) pR(0) vR(0) pC(0) vC(0) i(0)
Thus, a capacitor will resist changes in the potential difference across it because it requires a time t for the potential difference to change by vC. The potential difference across the capacitor decreases when it discharges and increases when charging. The larger the value of C, the slower the change in potential. If t is “small”, then to a good approximation, the potential difference across the capacitor at time t is An inductor can be considered to be a coil of wire. When a varying current passes through a coil, a varying magnetic flux is produced and this in turn induces a potential difference across the inductor. This induced potential difference opposes the change in current. The potential difference across the inductor is proportional to the rate of change of the current, where the constant of proportionality L is known as the inductance of the coil (henries H) and is given by the equation vL = L di/dt This equation can be expressed in terms of differences, iL(t) = vL(t) t / L Thus, an inductor will resist changes in the current through it because it requires a time t for the current to change by i. If t is “small”, then to a good approximation, the current through the inductor at time t is SERIES RC CIRCUIT Kirchhoff’s Laws with the equation can be used to compute the response of a series RC circuit for different applied emfs. The first step is calculate the applied emf vs and then specify the initial values for the variables for voltage v, current i, powers p and energies u. vS(0) vC(0) = 0 assume capacitor is initially discharged i(0) = { vS(0) – vC(0) } / R vR(0) = i(0) R pS(0) = vS(0) i(0) pR(0) = vR(0) i(0) pC(0) = vC(0) i(0)
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