Circuits with resistors and capacitors provide a good opportunity to examine energy conservation in circuits.  As the capacitor charges or discharges, the energy stored in the capacitor and the energy dissipated in the resistor both change.  Yet the total energy provided by the battery remains constant (assuming negligible losses due to the battery's own internal resistance).  We've seen that this fact of energy conservation is expressed in the loop rule.  The sum of the potential differences around the circuit is 0.  Consider the circuit of a battery, bulb (resistor), and capacitor in Figure 1.  The switch is initially open, and the capacitor is uncharged. There is no potential difference across the bulb or the capacitor, but there is a potential difference V_ab across the battery.  (We'll use V₁₂ to represent V₁ - V₂.)  When the switch is closed as in Figure 2, current flows in the circuit and charges the capacitor. The left-hand plate of the capacitor becomes positively charged, while the right-hand plate acquires an equal negative charge.  As charge builds up on the capacitor, so does the potential difference across it.  The potential difference across the resistor also changes with time as the amount of current in the circuit changes.  The current is maximum when the switch is closed and gradually diminishes to 0 when the capacitor is fully charged.  A graph of current vs. time is shown in Figure 3, while charge on the capacitor vs. time is shown in Figure 4.

Figure 1	Figure 2	Figure 3	Figure 4

The loop rule as applied to the circuit of Figure 2 is:  V_ab + V_ef + V_cd = 0.  Let's see which of these potential differences are positive and which are negative.

V_ab is positive, because point a is on the higher potential side of the battery.
V_ef is negative, because point e is on the low potential side of the bulb.
V_cd is negative, because point c is on the side of the capacitor with negative charge.

Thus, V_ab = -(V_ef + V_cd), where the terms in parentheses are negative.  Let's take away the negative sign in front of the parentheses and reverse the order of subscripts so that all the potential terms are positive.

V_ab = V_fe + V_dc

Now we'll plot a graph of all three potential differences vs. time from t = 0 until the capacitor is almost completely charged.  In the graph to the right, V_ab is constant, since that's the potential difference across the battery.  The potential difference V_dc across the capacitor is 0 initially when it's uncharged but increases asymptotically to the value of V_ab as it approaches its maximum charge. The potential difference V_fe across the resistor is maximum initially when the current is maximum but decreases asymptotically to 0.  Note that V_fe and V_dc are mirror images of each other about the dashed line.  This is a result of the conservation of energy.  The sum of V_dc and V_fe at any instant of time must be V_ab.