Kirchhoff's Loop Rule: The
algebraic sum of potential drops along a closed loop is equal to zero.
In the image to the left the potential (V) is analogous to height. According to the Loop Rule the potential difference caused by the battery () must be compensated for by the potential drops across the two resistors (r and R). Notice that the potential (V) starts at V_{a} and then returns again to V_{a} after resistor R. |
Q:
"A battery has an initial internal resistance of
0.75 and
an emf of 9 V. It is placed a cross a 5 resistor and
a 10 µF capacitor hooked up in parallel. A: First we will start off by drawing a picture of the circuit. a) After a the capacitor has
charged, what is the current through the resistor? R_{eq} = r + R
Because the resistors are in series, the current in this circuit, I, is constant and equal to the emf, , over the equivalent resistance, R_{eq}: I = / R_{eq} Now solve for I: The current through the battery is 1.57 A. b) What is the charge on the
capacitor? Q = CV_{R} = C (IR) = 10 µF (1.57 A) (5 ) = 78.3 µC. The charge on the capacitor is 78.3 µC. c) If the battery is
disconnected, how long will it take the capacitor to reach one-third of
its initial voltage? Since the capacitor is
discharging, the charge on it varies with time according to the equation
q(t) = Q e ^{(- t / RC)}.
To find the time, t, it takes the capacitor to reach one-third
of its initial capacity, we substitute q(t) = Q e ^{(- t / RC)} Q/3 = Q e ^{(- t / RC)} 1/3 = e ^{(- t / RC)} ln (1/3) = ln (e ^{(- t / RC)}) - ln 3 = - t / RC t = ( ln 3 ) (RC) t = (ln 3) (5 ) (10 µF) t = 54.9 µsec After 54.9 µsec, the capacitor has be one-third discharged. |
Q: If it is the current flowing through your body that determines the amount of damage done from a shock, why do the signs warn of high voltage and not high current? A: According to Ohm's Law ( I = V/R ), the current is proportional to voltage for a constant resistance. Therefore, with the resistance of the human body given, the larger the voltage the larger the current passing through the body. Contact with a high voltage source is thus more dangerous than with a low voltage source. |
[Top] [Previously Asked Questions] [References]
The Loop Rule: The algebraic sum of the charges in potential encountered in a complete traversal of any loop of a circuit must be zero.
The Junction Rule: The sum of the currents entering any junction must be equal to the sum of the currents leaving that junction.
Emf () | |
Single-loop circuits | |
Power | P = iV |
Rate of energy transfer to thermal energy within a battery | P_{r} = i^{2} r |
Rate of chemical energy change within a battery | P_{emf} = i |
Series resistances | |
Parallel Resistances | |
Charging capacitor | q = C ( 1 - e^{ - t/RC} ) |
Current during charging of the capacitor | |
Discharging capacitor | q = q_{0} e^{ - t/RC} |
Current during discharging of the capacitor |
[Top] [Previously Asked Questions] [References]
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