Electric Circuits
Beginner
Ohm's Law
Source: High school physics (Chinese)
Problem Sets:
ohm's law
Problem
A small light bulb has rated voltage $U_0 = 6$ V and rated power $P_0 = 18$ W. It is powered by a source with EMF $\varepsilon = 12$ V and internal resistance $r = 0.5\ \Omega$.
What resistance $R_s$ must be connected in series with the bulb so that the bulb operates at its rated values?
$R_s = 1.5\ \Omega$.
At rated operation, the current through the bulb is
$$I_0 = \frac{P_0}{U_0} = \frac{18}{6} = 3 \text{ A}.$$Applying Kirchhoff's voltage law around the single loop (the EMF drives current through the bulb, the series resistor, and the internal resistance):
$$\varepsilon = U_0 + I_0 R_s + I_0 r,$$so
$$R_s = \frac{\varepsilon - U_0}{I_0} - r = \frac{12 - 6}{3} - 0.5 = 2 - 0.5 = 1.5\ \Omega.$$