Electric Circuits
Beginner
Ohm's Law
Source: High school physics (Chinese)
Problem Sets:
ohm's law
Problem
A circuit requires a resistor of resistance $15$ k$\Omega$, but only several $10$ k$\Omega$ resistors are available.
How can the $10$ k$\Omega$ resistors be combined to obtain an equivalent resistance of $15$ k$\Omega$?
Use three $10$ k$\Omega$ resistors: two in parallel (giving $5$ k$\Omega$) in series with the third $10$ k$\Omega$, yielding $15$ k$\Omega$.
Connect two $10$ k$\Omega$ resistors in parallel:
$$R_\parallel = \frac{10 \times 10}{10 + 10} \text{ k}\Omega = 5 \text{ k}\Omega.$$Then place this parallel pair in series with one more $10$ k$\Omega$ resistor:
$$R_\text{total} = 5 \text{ k}\Omega + 10 \text{ k}\Omega = 15 \text{ k}\Omega.$$Three $10$ k$\Omega$ resistors are required in total.