# Join the resistance!

**Electricity and Magnetism**Level 1

In a circuit we have three resistances, \({ R }_{ 1 }\), \({ R }_{ 2 }\) and \({ R }_{ 3 }\). It's known that \({ R }_{ 1 }=a\), \({ R }_{ 2 }={ a }^{ 2 }\) and \({ R }_{ 3 }={ a }^{ 3 }\). Also we know that if we create a parallel circuit with \({ R }_{ 1 }\), \({ R }_{ 2 }\) and \({ R }_{ 3 }\) the total resistance is \({ R }_{ p }\) but if we create a series circuit with them, the total resistance is \({ R }_{ s }\). If \(9{ R }_{ p }={ R }_{ s }\), calculate the value of \({ R }_{ 1 }\).