Peoples Physics Book Version-2

14.2. Circuit Basics http://www.ck12.org

For sources of constant voltage, such as batteries, the current varies with resistance:

I=

V

R

[3]

Unlike equation [1], whereRvaried with current, we can use equation [2] to find the current, voltage drop, or
resistance across a resistor when given the other two. When dealing with a constant current, use equation [2], but
when dealing with a battery driven circuit (a source of constant voltage difference), use equation [3].

Power

Poweris the rate at which energy is lost by a system. The units of power are Watts (W), which equal Joules per
second(1W = 1J/s). Therefore, a 60 W light bulb releases 60 Joules of energy every second.

The equation used to calculate thepowerdissipated in a circuit or across a resistor is:

P=IV= ︸︷︷︸I^2 R

SinceV=IR

[4] Power Dissipated Through a Voltage Drop

As with OhmÕs Law, one must be careful not to mix apples with oranges. If you want the power of the entire circuit,
then you multiply thetotalvoltage of the power source by thetotalcurrent coming out of the power source. If you
want the power dissipated (i.e. released) by a light bulb, then you multiply thevoltage dropacross the light bulb by
thecurrent going through that light bulb.

Resistors in Series and in Parallel

Sometimes, circuits have many resistors in various geometrical arrangements. Whenin series, two or more resistors
are connected end to end (See picture). In this case the resistors receive the same current, but since they can have
different resistances they may have different voltage drops across them. Analogously, there may be more rocks at
some points in the river than in others, but if there is only one way for the river to flow, the current has to be the same
at all points. It follows from Ohm’s law that

Rtotal=R 1 +R 2 +R 3 +... [5] Resistors in Series

Since the total resistance willincreasewith each resistor added in series, adding resistors in series will cause the less
current to flow at a set voltage (according to Ohm’s Law for constant voltage sources, [3]).

When two or more resistors are connected together at both ends, they are said to be "in parallel" (see picture). There
are many rivers (the river splits into streams), so all resistors receive different amounts of current. But since they
all connect the same points on the circuit, the voltage drops across them have to be equal. The rule for combining
resistors in parallel is

1

Rtotal

=

1

R 1

+

1

R 2

+

1

R 3

+... [6] Resistors in Parallel

Since the total resistance willdecreasewith the number or resistors in parallel, adding resistors in parallel to existing
ones will cause more current to flow through a circuit.