The unit of current is the ampere (A), or amp for short. A thousandth of an amp is a milliamp (mA). One amp is equal to one coulomb of charge per second.
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It will not be possible to measure current unless the circuit is powered and operating.
The current measured at any point in a simple circuit will be the same because current is the measure of electron flow through a circuit. The current flowing through any branch of any circuit (or an entire simple circuit) will always be the same at any point.
The flow in a circuit is called the electric current and it is measured by voltages. The number of volts that are present in the charge will determine the strength of the electric current.
Assuming you are talking about an AC circuit, then the total opposition to the flow of current in an R-C circuit is called its impedance (symbol: Z), measured in ohms. This is the vector sum of the circuit's resistance (R) and its capacitive reactance (XC) -each also measured in ohms.
This is most easily done using an oscilloscope with a current probe. Also phase angle must be measured relative to something else, usually the AC voltage at one end or the other of the branch of the circuit where the current is being measured.