## review derivation: total electrical resistance for circuit with two resistors in series

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Notes for this derivation:
http://www.dfcd.net/articles/derivations/resistors.html

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
7 divide both sides by
1. 2715678478; locally 4870091:
$$I R_{\rm total} = I R_1 + I R_2$$
$$pdg_{1908} pdg_{4501} = pdg_{3461} pdg_{4501} + pdg_{4501} pdg_{8697}$$
1. 7844317489:
$$I$$
$$pdg_{4501}$$
1. 7217021879; locally 5454988:
$$R_{\rm total} = R_1 + R_2$$
$$pdg_{1908} = pdg_{3461} + pdg_{8697}$$
valid 2715678478:
7217021879:
2715678478:
7217021879:
2 change two variables in expr
1. 4087145886; locally 3843961:
$$V = I R$$
$$pdg_{6599} = pdg_{4501} pdg_{6458}$$
1. 2698469612:
$$V$$
$$pdg_{6599}$$
2. 9830343096:
$$V_1$$
$$pdg_{8257}$$
3. 7774819339:
$$R$$
$$pdg_{6458}$$
4. 9174439158:
$$R_1$$
$$pdg_{8697}$$
1. 7675171493; locally 8012785:
$$V_1 = I R_1$$
$$pdg_{8257} = pdg_{4501} pdg_{8697}$$
valid 4087145886:
7675171493:
4087145886:
7675171493:
I is the same across both resistors
3 change two variables in expr
1. 4087145886; locally 3843961:
$$V = I R$$
$$pdg_{6599} = pdg_{4501} pdg_{6458}$$
1. 7497687256:
$$V$$
$$pdg_{6599}$$
2. 1608399874:
$$V_2$$
$$pdg_{8721}$$
3. 5890617067:
$$R$$
$$pdg_{6458}$$
4. 1484794622:
$$R_2$$
$$pdg_{3461}$$
1. 6061695358; locally 6379878:
$$V_2 = I R_2$$
$$pdg_{8721} = pdg_{3461} pdg_{4501}$$
valid 4087145886:
6061695358:
4087145886:
6061695358:
6 substitute LHS of three expressions into expr
1. 4939880586; locally 4107950:
$$V_{\rm total} = I R_{\rm total}$$
$$pdg_{4691} = pdg_{1908} pdg_{4501}$$
2. 7675171493; locally 8012785:
$$V_1 = I R_1$$
$$pdg_{8257} = pdg_{4501} pdg_{8697}$$
3. 6061695358; locally 6379878:
$$V_2 = I R_2$$
$$pdg_{8721} = pdg_{3461} pdg_{4501}$$
4. 9063568209; locally 1124189:
$$V_{\rm total} = V_1 + V_2$$
$$pdg_{4691} = pdg_{8257} + pdg_{8721}$$
1. 2715678478; locally 4870091:
$$I R_{\rm total} = I R_1 + I R_2$$
$$pdg_{1908} pdg_{4501} = pdg_{3461} pdg_{4501} + pdg_{4501} pdg_{8697}$$
no check performed 4939880586:
7675171493:
6061695358:
9063568209: failed
2715678478:
4939880586:
7675171493:
6061695358:
9063568209: N/A
2715678478:
1 declare initial expr
1. 4087145886; locally 3843961:
$$V = I R$$
$$pdg_{6599} = pdg_{4501} pdg_{6458}$$
no validation is available for declarations 4087145886:
4087145886:
5 declare initial expr
1. 4939880586; locally 4107950:
$$V_{\rm total} = I R_{\rm total}$$
$$pdg_{4691} = pdg_{1908} pdg_{4501}$$
no validation is available for declarations 4939880586:
4939880586:
8 declare final expr
1. 7217021879; locally 5454988:
$$R_{\rm total} = R_1 + R_2$$
$$pdg_{1908} = pdg_{3461} + pdg_{8697}$$
no validation is available for declarations 7217021879:
7217021879:
4 declare initial expr
1. 9063568209; locally 1124189:
$$V_{\rm total} = V_1 + V_2$$
$$pdg_{4691} = pdg_{8257} + pdg_{8721}$$
no validation is available for declarations 9063568209: failed
9063568209: N/A
voltage is measured across both resistors
Physics Derivation Graph: Steps for total electrical resistance for circuit with two resistors in series

## Symbols for this derivation

symbol ID category latex scope dimension name value Used in derivations references
4501 variable I
$$I$$
real
• electric charge: 1
• time: -1
electric current
9
1908 variable R_{\rm total}
$$R_{\rm total}$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
9
8721 variable V_2
$$V_2$$
real
• electric charge: -1
• length: 2
• mass: 1
• time: -2
voltage
3
8697 variable R_1
$$R_1$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
10
4691 variable V_{\rm total}
$$V_{\rm total}$$
real
• electric charge: -1
• length: 2
• mass: 1
• time: -2
voltage
2
3461 variable R_2
$$R_2$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
10
8257 variable V_1
$$V_1$$
real
• electric charge: -1
• length: 2
• mass: 1
• time: -2
voltage
3
6458 variable R
$$R$$
real
• electric charge: -2
• length: 2
• mass: 1
• time: -1
electrical resistance
6
6599 variable V
$$V$$
real
• electric charge: -1
• length: 2
• mass: 1
• time: -2
voltage
11
MESSAGES:
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• in step 2247327: name 'electric_charge' is not defined
• in step 2247327: name 'electric_charge' is not defined
• in step 2247327: name 'electric_charge' is not defined
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