Unit 6: Direct-Current Circuits
EMF sources, resistor networks too tangled for series or parallel shortcuts, two rules that solve them anyway, and a capacitor charging on its own exponential.
10 topics · 35 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
EMF and Internal Resistance
- How it worksHow does a battery's own internal resistance eat part of its emf before any of it reaches the circuit?
- Worked exampleFind the terminal voltage of a 12 volt battery with 0.5 ohms internal resistance delivering 2 amps.
- Common mistakeWhy isn't a battery's emf the same thing as its terminal voltage the moment current starts flowing?
- Going furtherWhat happens to a battery's terminal voltage as the external resistance it drives grows very large?
- Worked exampleFind the current a 6 volt battery with 1 ohm internal resistance drives through a short circuit of zero external resistance.
Your turn1 of 2
Find the terminal voltage of a 19 volt battery with 4 ohms internal resistance delivering 9 amps.Resistors in Series
- How it worksHow do resistors in series end up sharing the same current while splitting up the total voltage?
- Worked exampleFind the equivalent resistance of a 10, a 20, and a 30 ohm resistor connected in series.
- Common mistakeWhy doesn't current keep flowing through the rest of a series circuit once any single point in it breaks?
Your turn1 of 2
Find the equivalent resistance of a 71, a 67, and a 94 ohm resistor connected in series.Resistors in Parallel
- How it worksHow do resistors in parallel end up sharing the same voltage while splitting up the total current?
- Worked exampleFind the equivalent resistance of a 6 ohm and a 12 ohm resistor connected in parallel.
- Going furtherWhat happens to a parallel combination's equivalent resistance as you keep adding more branches to it?
Your turn1 of 2
Find the equivalent resistance of a 71 ohm and a 67 ohm resistor connected in parallel.Kirchhoff's Junction Rule
- How it worksHow does the junction rule turn conservation of charge into an equation you can write at every node?
- Worked exampleFind the current in the third wire at a junction where 3 amps and 5 amps flow in and only one wire carries current out.
- Ties togetherHow does the junction rule generalize the plain series and parallel current rules to any circuit shape?
Your turn1 of 2
At a junction, 14 amps and 13 amps flow in, and only one wire carries current out. Find the current in that third wire.Kirchhoff's Loop Rule
- How it worksHow does the loop rule turn conservation of energy into an equation you can write around any closed path?
- Worked exampleFind the current in a single loop with a 9 volt battery and a 10 ohm and a 20 ohm resistor in series.
- Ties togetherHow do the junction rule and the loop rule together solve circuits that series and parallel shortcuts can't touch?
Your turn1 of 2
Find the current in a single loop with a 18 volt battery and a 34 ohm and a 47 ohm resistor in series.Solving a Multiloop Circuit with Kirchhoff's Rules
- How it worksHow do you assign current variables and directions before writing Kirchhoff's rules for a multiloop circuit?
- How it worksWalk me through picking enough independent loop and junction equations to solve for every current.
- Worked exampleFind the three branch currents in a two-loop circuit with a 10 volt and a 5 volt battery and resistors of 2, 3, and 4 ohms.
- Going furtherWhat happens to your final answer if you guess the wrong direction for one branch current at the start?
Your turn1 of 2
A two-loop circuit has a 15 volt battery in series with a 9 ohm resistor forming one branch, a 14 volt battery in series with a 4 ohm resistor forming a second branch, and both branches connect across a shared 3 ohm resistor. Find the current through the shared resistor.Ammeters and Voltmeters
- How it worksHow does an ammeter's near-zero resistance let it sit in series without disturbing a circuit's current?
- Common mistakeWhy isn't a voltmeter ever wired in series with the component whose voltage you want to measure?
- Common mistakeWhy doesn't an ideal voltmeter draw any current away from the branch of the circuit it's measuring?
Your turn1 of 2
An ammeter is accidentally wired in parallel with a resistor instead of in series with it. What is the likely result?An RC Circuit Charging
- How it worksHow does the current in a charging RC circuit decay exponentially as the capacitor's own voltage builds?
- Worked exampleFind the voltage across a 10 microfarad capacitor 0.02 seconds after a 5 volt battery starts charging it through a 1000 ohm resistor.
- Common mistakeWhy doesn't a charging capacitor ever reach its final voltage in some fixed, finite amount of time?
- Going furtherWhat happens to an RC circuit's charging curve if the resistance in the circuit is made much larger?
- Ties togetherHow does the time constant RC set the timescale over which a capacitor visibly charges or discharges?
Your turn1 of 2
Find the voltage across a 15 microfarad capacitor 47 milliseconds after a 9 volt battery starts charging it through a 1473 ohm resistor.An RC Circuit Discharging
- How it worksHow does a discharging capacitor's own shrinking voltage slow down the very current that's draining it?
- Worked exampleFind the charge remaining on a 20 microfarad capacitor, started at 100 microcoulombs, 0.05 seconds after it starts discharging through a 2000 ohm resistor.
- Going furtherWhat happens to how quickly a capacitor discharges if the resistance in its circuit is doubled?
Your turn1 of 2
Find the charge remaining on a 36 microfarad capacitor, started at 137 microcoulombs, 30 milliseconds after it starts discharging through a 2831 ohm resistor.Household Wiring and Electrical Safety
- How it worksHow does wiring every household outlet in parallel keep one failed appliance from cutting power to the rest?
- How it worksWalk me through how a fuse senses too much current and opens a circuit before its wires can overheat.
- Ties togetherHow does a house's parallel wiring connect back to why parallel resistors lower a circuit's total resistance?
Your turn1 of 2
Plugging one more appliance into an already-loaded outlet circuit trips the circuit breaker. Why does adding another appliance, wired in parallel with the others, increase the risk of overload?