The tuned circuit the Oscillator in a simple AM transmitter employs a `50mu H` coil and a 1 nF capacitor. If the oscillator output is modulated by audio frequencies up to 10m kHz calculate the range occupied by the side bands. 

Explanation

To solve the problem, we need to calculate the carrier frequency (fc) of the oscillator circuit formed by the given inductor (L) and capacitor (C), and then determine the lower sideband (LSB) and upper sideband (USB) frequencies based on the modulating frequency (fm).

### Step-by-Step Solution:

1. **Identify Given Values:**
- Inductance (L) = 50 µH = \(50 \times 10^{-6}\) H
- Capacitance (C) = 1 nF = \(1 \times 10^{-9}\) F
- Modulating frequency (fm) = 10 kHz = \(10 \times 10^{3}\) Hz
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