Circuit There are two types of circuits that we covered in this lab. One type is an RC circuit, which has a power supply, a resistor, and a capacitor. The other type is an LR circuit, which has a power supply, an inductor, and a resistor. The first was an RC circuit. The capacitance (C) of a capacitor is equal to the charge (Q) on each plate divided by the potential difference (VC) between the plates. C º Q / VC Capacitance has the unit of farad (F). Using Kirchoff's circuit rule, we know that the voltage drop across the resistor (VR) plus the voltage drop across the capacitor (VC) equals the voltage rise across the battery (x). This equation is: VR + VC = x Using Ohm's law and the definition of current we get: VR = IR I = DQ / Dt Therefore: VR = (DQ / Dt )RU Using the information above, we can rewrite the rule of the Kirchoff cycle, which looks like: R(DQ / Dt) + (Q / C) = xSubstituting the following variables x and t, we can look at the equation in a different way. Here are the definitions of these variables:x º Q - xC t º RCTo obtain the charge as a function of time, we use this equationDx / Dt = - x / t Graphing x versus time, we get the following equation:x = x0 e( -t / t)x0 is the value of x at = 0. If we replace x in the previous equation with the definition of x, we get:Q = Q¥ (1 - e(-t / t) )Substituting the previous equation in the equation for capacitance and resistance, we get: VC = x(1 - e(-t / t)) VR = xe(-t / t) Since the current (I) is VR / R, we can get the equation : I = I0e(-t / t) The discharge of a capacitor in an RC circuit can also be related to time. This is seen in the following equation:DQ / Dt = - Q / tRelating this equation to a similar equation we defined earlier, we can get:Q = Q0e(-t / t)Using the capacitance definition and the loop rule Kirchoff equation, we can expand the previous equation to these equations:VC = xe(-t / t) VR = -xe(-t / t)Using the definition of current, we get:I = -I0e(-t / t) The other circuit type was an LR circuit. The back emf (xL) is equal to the rate of change of the current multiplied by the coil inductance (L).