Electrical resistance is the tendency of a material to oppose the flow of an electric current. We use the symbol, $R$ to represent resistance. The SI unit is the Ohm ($\Omega$).
Ohm’s Law
This states that the current flowing through a conductor is directly proportional to the voltage across its ends, given that the temperature remains constant. This proportionality can be represented as:
$$V\propto I$$
By introducing the constant of proportionality, $R$, we get: $$V=IR$$ This is the equation commonly used when referring to Ohm’s Law - resistance is simply the ratio of the voltage applied to the current flowing through a material.
Equivalent resistance in series circuits
Three resistors placed in series, with resistances $R_1$, $R_2$, $R_3$, can be replaced by a single resistor of resistance $R_T$: $$ \begin{equation}\begin{aligned} R_T=R_1+R_2+R_3\\ \end{aligned}\end{equation} $$
What do you think?
1) What is the resistance of the resistor that can be used to replace resistors in series, with resistances, $3 \Omega$, $4 \Omega$ and $7 \Omega$?
- $14 \Omega$
- $0 \Omega$
- $8 \Omega$
- $7 \Omega$
$R_T=3\Omega + 4\Omega +7\Omega=14\Omega$
Equivalent resistance in parallel circuits
Three resistors placed in parallel, with resistances $R_1$, $R_2$, $R_3$, can be replaced by a single resistor of resistance $R_T$: $$ \begin{equation}\begin{aligned} \frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\\ \end{aligned}\end{equation} $$
What do you think?
2) What is the equivalent resistance of two resistors, $2\Omega$ and $4\Omega$ wired in parallel?
- $1.33\Omega$
- $0.75\Omega$
- $2\Omega$
- $6\Omega$
$$\frac{1}{R_T}=\frac{1}{2\Omega}+\frac{1}{4\Omega}=\frac{3}{4\Omega}\\ \rightarrow R_T=\frac{4\Omega}{3}$$
Temperature can affect resistance
Ohm’s Law mentions the constraint that temperature must be unchanged in order for the current to vary proportionally to the applied voltage.
Thus, resistance can be used as a thermometric property because it varies with temperature. A temperature sensitive resistor is called a thermistor.
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