Circuits

1. Circuits Electromotive Force Work, Energy and emf Current in a Simple Loop Potential Difference Between Two Points A Real Battery Multi-loop Circuits Ammeters and Voltmeters RC Circuits

2. Direct current circuits (DC) are those in which the current move only in one direction due to the potential difference induced by the battery. The battery acts as a pump moving the charge through the conductor. The battery is an emf device or seat of emf. The emf stands for electromotive force, a term which is rarely used now. Other emf devices include electric generators, solar cells and fuel cells. All these devices maintain a potential difference. An emf device provides energy to do work on the charges, moving them through the conductor. The emf is represented by E. An ideal emf device has no internal resistance to the movement of charges inside the device. A real emf device like a battery has internal resistance. When the battery is not connected to a circuit, the potential difference between its terminals is equal to its emf. However, when a current is moving through the device, the potential difference is different from its emf. Using energy considerations, the current can be determined. Kirchhoff’s Loop Rule states that the sum of the changes in potential difference around a complete circuit loop must be zero.

3. When a current moves through a resistor, the change in potential is -R. If one moves in the opposite direction of the current, the change in potential is + R. If one moves through an ideal emf device in the direction of the current, the change in potential is + E. If one moves in the opposite direction through the emf device, the change in potential is - E. The internal resistance in the emf device is designated by r. Recall that the internal resistance exists only when a current flows through a circuit. When a potential difference, V, is applied across resistances connected in series, the resistances have identical currents, . The sum of the potential differences across all the resistors is equal to the applied potential difference, V. Resistances connected in series can be replaced by an equivalent resistance which is equal to the sum of the resistances. The equivalent resistance has the same current, , and the same total potential difference, V, as the actual resistances.

4. This equivalent resistance can be written as To find the potential difference between any two points in a circuit, start at one point and follow the circuit to the other point, along any path, and add algebraically the changes in potential difference as they are encountered. The potential difference across the terminals of a real battery is equal to the emf minus the current multiplied by the internal resistance. Grounding a circuit means connecting it to the earth. The earth is defined as a zero potential. The power of the emf device is the first term. The internal power dissipation rate is the last term. The junction rule states that the sum of the current entering any junction must equal the sum of the currents leaving the junction. When a potential difference, V, is applied across resistors connected in parallel, the resistances all have the same potential difference, V.

5. Resistances connected in parallel can be replaced with an equivalent resistance that has the same potential difference, V, and the same total current, , as the actual resistances. An ammeter measures the current in a circuit. Thus the ammeter must be connected in series with the resistors in order that all the current passes through the meter. So as not to change the current, the resistance of the ammeter must be much smaller than the resistance of the remainder of the circuit. A voltmeter measures the potential difference across any element of the circuit. The voltmeter must be placed in parallel with the element being measured. The resistance of the voltmeter must be very high so that very little current will pass through the meter. An RC circuit is one that contains a resistor, a capacitor and an ideal battery. One can write an equation for the potential difference around the circuit.

6. The last equation is a differential equation because it contains the quantity, its derivative and a constant. The answer is an exponential equation. If one takes the derivative of the charge with respect to time, one finds the current. Dividing the charge by the capacitance gives the potential while charging the capacitor. In each of these equations, there is the quantity, RC, the capacitive time constant. When the RC circuit is being discharged, the emf is no longer in the equation.