Kirchhoff's Rules for Multi-Loop Circuits · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Solving circuits with two rules

Science · Electricity & Magnetism · ages 19-20
Name ______________________   Date ____________

  1. What does the loop rule state?

    • The voltage changes around a closed loop sum to zero
    • The currents in parallel branches are equal
    • Each loop carries the same current

  2. What does the junction rule state?

    • Voltages around a loop sum to zero
    • Currents entering equal currents leaving
    • Resistances in series add up

  3. The junction rule rests on charge conservation and the loop rule on energy conservation.

    Circle one:   True   False

  4. Junction b gives I1 equals I2 plus I3. What does junction e add?

    • A fully independent second equation
    • The same relation written as I2 plus I3 equals I1
    • A loop equation for the outer loop

  5. A 9 V battery drives a loop with 1, 2 and 6 ohm resistors in series. Give the current in A.

    Answer: ______________

  6. You cross a resistor against its assigned current. What is the voltage change?

    • Minus I times R
    • Zero, since you moved backwards
    • Plus I times R

  7. 2 A enters a junction. 0.75 A leaves through one branch. Give the current leaving through the other branch in A.

    Answer: ______________

  8. A branch current solves to minus 0.5 A. What does that mean?

    • No current flows in that branch
    • The current truly runs opposite the arrow
    • The loop equations were set up wrong
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Solving circuits with two rules W1-mt_AS3KiGstGD-s1

  1. The voltage changes around a closed loop sum to zero · Loops conserve energy, so gains and drops cancel round a loop.
  2. Currents entering equal currents leaving · Junctions conserve charge, so what flows in must flow out.
  3. True · Charge gives the junction rule and energy gives the loop rule.
  4. The same relation written as I2 plus I3 equals I1 · The two junction equations carry the same content, so only one counts.
  5. 1 · Loop rule gives 9 minus 9 I equals zero, so I is 1.
  6. Plus I times R · Moving against the current climbs the potential by I R.
  7. 1.25 · Junction rule gives 2 minus 0.75, which is 1.25.
  8. The current truly runs opposite the arrow · The size is right and only the guessed direction was backwards.
Worksheet · LightMySky